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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 334620.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 334620.bs1 | 334620bs2 | \([0, 0, 0, -91767, -10673026]\) | \(94875856/275\) | \(247719560774400\) | \([2]\) | \(1354752\) | \(1.6327\) | |
| 334620.bs2 | 334620bs1 | \([0, 0, 0, -8112, -15379]\) | \(1048576/605\) | \(34061439606480\) | \([2]\) | \(677376\) | \(1.2861\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 334620.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 334620.bs do not have complex multiplication.Modular form 334620.2.a.bs
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.
