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SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 430950.hv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 430950.hv1 | 430950hv1 | \([1, 0, 0, -87188, -9913008]\) | \(2135227170133/832320\) | \(28571985000000\) | \([2]\) | \(1548288\) | \(1.5469\) | \(\Gamma_0(N)\)-optimal |
| 430950.hv2 | 430950hv2 | \([1, 0, 0, -74188, -12968008]\) | \(-1315451937493/1353040200\) | \(-46447333115625000\) | \([2]\) | \(3096576\) | \(1.8935\) |
Rank
sage: E.rank()
The elliptic curves in class 430950.hv have rank \(1\).
Complex multiplication
The elliptic curves in class 430950.hv do not have complex multiplication.Modular form 430950.2.a.hv
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.
