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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 57330.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57330.dv1 | 57330eg4 | \([1, -1, 1, -38159078, 90738287637]\) | \(71647584155243142409/10140000\) | \(869668466940000\) | \([2]\) | \(2949120\) | \(2.7195\) | |
| 57330.dv2 | 57330eg3 | \([1, -1, 1, -2737958, 971178261]\) | \(26465989780414729/10571870144160\) | \(906708293980314003360\) | \([2]\) | \(2949120\) | \(2.7195\) | |
| 57330.dv3 | 57330eg2 | \([1, -1, 1, -2385158, 1417964181]\) | \(17496824387403529/6580454400\) | \(564380048305382400\) | \([2, 2]\) | \(1474560\) | \(2.3730\) | |
| 57330.dv4 | 57330eg1 | \([1, -1, 1, -127238, 28891797]\) | \(-2656166199049/2658140160\) | \(-227978370597519360\) | \([2]\) | \(737280\) | \(2.0264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57330.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 57330.dv do not have complex multiplication.Modular form 57330.2.a.dv
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.
