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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 379456.iz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 379456.iz1 | 379456iz2 | \([0, -1, 0, -540542977, 3392923769985]\) | \(1278763167594532/375974556419\) | \(5135500043993349668293246976\) | \([2]\) | \(176947200\) | \(4.0230\) | |
| 379456.iz2 | 379456iz1 | \([0, -1, 0, 90776943, 352865827217]\) | \(24226243449392/29774625727\) | \(-101674161934835907783933952\) | \([2]\) | \(88473600\) | \(3.6764\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 379456.iz have rank \(1\).
Complex multiplication
The elliptic curves in class 379456.iz do not have complex multiplication.Modular form 379456.2.a.iz
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.
