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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 311696.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 311696.bs1 | 311696bs2 | \([0, 0, 0, -118459, 15692490]\) | \(50668941906/1127\) | \(4088932857856\) | \([2]\) | \(737280\) | \(1.5349\) | |
| 311696.bs2 | 311696bs1 | \([0, 0, 0, -7139, 263538]\) | \(-22180932/3703\) | \(-6717532552192\) | \([2]\) | \(368640\) | \(1.1883\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 311696.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 311696.bs do not have complex multiplication.Modular form 311696.2.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.
