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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 57960.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.bf1 | 57960bs1 | \([0, 0, 0, -9499647, -10855002814]\) | \(508017439289666674384/21234429931640625\) | \(3962854251562500000000\) | \([2]\) | \(3440640\) | \(2.9092\) | \(\Gamma_0(N)\)-optimal |
| 57960.bf2 | 57960bs2 | \([0, 0, 0, 4562853, -40248440314]\) | \(14073614784514581404/945607964406328125\) | \(-705892562997466320000000\) | \([2]\) | \(6881280\) | \(3.2557\) |
Rank
sage: E.rank()
The elliptic curves in class 57960.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 57960.bf do not have complex multiplication.Modular form 57960.2.a.bf
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.
