Opened 8 years ago

Closed 8 years ago

## #17293 closed defect (fixed)

# Taking the dual of a negated isogeny raises an error

Reported by: | Peter Bruin | Owned by: | |
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Priority: | minor | Milestone: | sage-6.4 |

Component: | elliptic curves | Keywords: | isogeny dual |

Cc: | Merged in: | ||

Authors: | Peter Bruin | Reviewers: | Frédéric Chapoton |

Report Upstream: | N/A | Work issues: | |

Branch: | f40eb90 (Commits, GitHub, GitLab) | Commit: | f40eb909f4545d5c99288dbe33bbac1dc17bc4e5 |

Dependencies: | Stopgaps: |

### Description (last modified by )

In the following example, taking the dual works for the isogeny `phi`

but fails for the negated isogeny `psi`

:

sage: k.<s> = QuadraticField(2) sage: E = EllipticCurve(k, [-3*s*(4 + 5*s), 2*s*(2 + 14*s + 11*s^2)]) sage: phi = E.isogenies_prime_degree(3)[0] sage: psi = -phi sage: phi.dual() Isogeny of degree 3 from Elliptic Curve defined by y^2 = x^3 + (108*s-270)*x + (-1296*s+1512) over Number Field in s with defining polynomial x^2 - 2 to Elliptic Curve defined by y^2 = x^3 + (-12*s-30)*x + (48*s+56) over Number Field in s with defining polynomial x^2 - 2 sage: psi.dual() Traceback (most recent call last): ... NameError: global name 'E0' is not defined

There is also a (trivial) bug that causes the dual to remain cached if the isogeny is changed by precomposing or postcomposing with an isomorphism (which is the way negation is implemented):

sage: -(phi.dual()) == (-phi).dual() False

### Change History (4)

### comment:1 Changed 8 years ago by

Description: | modified (diff) |
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### comment:2 Changed 8 years ago by

Authors: | → Peter Bruin |
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Branch: | → u/pbruin/17293-isogeny_dual_negate |

Commit: | → f40eb909f4545d5c99288dbe33bbac1dc17bc4e5 |

Status: | new → needs_review |

### comment:3 Changed 8 years ago by

Reviewers: | → Frédéric Chapoton |
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Status: | needs_review → positive_review |

### comment:4 Changed 8 years ago by

Branch: | u/pbruin/17293-isogeny_dual_negate → f40eb909f4545d5c99288dbe33bbac1dc17bc4e5 |
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Resolution: | → fixed |

Status: | positive_review → closed |

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LGTM