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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 7488bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7488.q2 | 7488bc1 | \([0, 0, 0, 69, -340]\) | \(778688/1521\) | \(-70963776\) | \([2]\) | \(2048\) | \(0.19101\) | \(\Gamma_0(N)\)-optimal |
7488.q1 | 7488bc2 | \([0, 0, 0, -516, -3616]\) | \(5088448/1053\) | \(3144241152\) | \([2]\) | \(4096\) | \(0.53758\) |
Rank
sage: E.rank()
The elliptic curves in class 7488bc have rank \(1\).
Complex multiplication
The elliptic curves in class 7488bc do not have complex multiplication.Modular form 7488.2.a.bc
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 Cremona 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 Cremona labels.