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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 344760.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 344760.m1 | 344760m1 | \([0, -1, 0, -16511356, -25045539884]\) | \(402876451435348816/13746755117745\) | \(16986358098720672180480\) | \([2]\) | \(30965760\) | \(3.0376\) | \(\Gamma_0(N)\)-optimal |
| 344760.m2 | 344760m2 | \([0, -1, 0, 5664824, -87342864740]\) | \(4067455675907516/669098843633025\) | \(-3307123016025577233638400\) | \([2]\) | \(61931520\) | \(3.3841\) |
Rank
sage: E.rank()
The elliptic curves in class 344760.m have rank \(0\).
Complex multiplication
The elliptic curves in class 344760.m do not have complex multiplication.Modular form 344760.2.a.m
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
