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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 364650.ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 364650.ed1 | 364650ed3 | \([1, 1, 1, -1370213, 616414031]\) | \(18208239480684565129/12399505944540\) | \(193742280383437500\) | \([4]\) | \(5898240\) | \(2.2548\) | |
| 364650.ed2 | 364650ed2 | \([1, 1, 1, -102713, 5479031]\) | \(7669732067600329/3595498592400\) | \(56179665506250000\) | \([2, 2]\) | \(2949120\) | \(1.9083\) | |
| 364650.ed3 | 364650ed1 | \([1, 1, 1, -52713, -4620969]\) | \(1036710271472329/15169440000\) | \(237022500000000\) | \([2]\) | \(1474560\) | \(1.5617\) | \(\Gamma_0(N)\)-optimal |
| 364650.ed4 | 364650ed4 | \([1, 1, 1, 364787, 41944031]\) | \(343575091109876471/247117464619740\) | \(-3861210384683437500\) | \([2]\) | \(5898240\) | \(2.2548\) |
Rank
sage: E.rank()
The elliptic curves in class 364650.ed have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.ed do not have complex multiplication.Modular form 364650.2.a.ed
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
