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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 402930c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
402930.c2 | 402930c1 | \([1, -1, 0, 1380, 11600]\) | \(299418309/236800\) | \(-229766803200\) | \([2]\) | \(737280\) | \(0.86797\) | \(\Gamma_0(N)\)-optimal* |
402930.c1 | 402930c2 | \([1, -1, 0, -6540, 105056]\) | \(31885169211/13690000\) | \(13283393310000\) | \([2]\) | \(1474560\) | \(1.2145\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 402930c have rank \(2\).
Complex multiplication
The elliptic curves in class 402930c do not have complex multiplication.Modular form 402930.2.a.c
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.