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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 129960.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129960.x1 | 129960o4 | \([0, 0, 0, -98770683, 377824571782]\) | \(3034301922374404/1425\) | \(50045375825740800\) | \([2]\) | \(5898240\) | \(2.9780\) | |
| 129960.x2 | 129960o3 | \([0, 0, 0, -7408803, 3372721198]\) | \(1280615525284/601171875\) | \(21112892926484400000000\) | \([2]\) | \(5898240\) | \(2.9780\) | |
| 129960.x3 | 129960o2 | \([0, 0, 0, -6174183, 5901469882]\) | \(2964647793616/2030625\) | \(17828665137920160000\) | \([2, 2]\) | \(2949120\) | \(2.6314\) | |
| 129960.x4 | 129960o1 | \([0, 0, 0, -309738, 129683113]\) | \(-5988775936/9774075\) | \(-5363456762324314800\) | \([2]\) | \(1474560\) | \(2.2848\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129960.x have rank \(1\).
Complex multiplication
The elliptic curves in class 129960.x do not have complex multiplication.Modular form 129960.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
