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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 81120bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81120.f2 | 81120bc1 | \([0, -1, 0, 1634, 6616]\) | \(1560896/975\) | \(-301192881600\) | \([2]\) | \(64512\) | \(0.89166\) | \(\Gamma_0(N)\)-optimal |
| 81120.f1 | 81120bc2 | \([0, -1, 0, -6816, 60696]\) | \(14172488/7605\) | \(18794435811840\) | \([2]\) | \(129024\) | \(1.2382\) |
Rank
sage: E.rank()
The elliptic curves in class 81120bc have rank \(0\).
Complex multiplication
The elliptic curves in class 81120bc do not have complex multiplication.Modular form 81120.2.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.
