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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 397800.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.dv1 | 397800dv1 | \([0, 0, 0, -1408575, -643454750]\) | \(105992740376656/18785\) | \(54777060000000\) | \([2]\) | \(4128768\) | \(2.0327\) | \(\Gamma_0(N)\)-optimal |
| 397800.dv2 | 397800dv2 | \([0, 0, 0, -1404075, -647770250]\) | \(-26245032877444/352876225\) | \(-4115948288400000000\) | \([2]\) | \(8257536\) | \(2.3792\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.dv have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.dv do not have complex multiplication.Modular form 397800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
