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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 41280c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.r1 | 41280c1 | \([0, -1, 0, -1481, 22281]\) | \(87765160384/725625\) | \(2972160000\) | \([2]\) | \(24576\) | \(0.64387\) | \(\Gamma_0(N)\)-optimal |
41280.r2 | 41280c2 | \([0, -1, 0, -481, 50881]\) | \(-376367048/33698025\) | \(-1104216883200\) | \([2]\) | \(49152\) | \(0.99045\) |
Rank
sage: E.rank()
The elliptic curves in class 41280c have rank \(1\).
Complex multiplication
The elliptic curves in class 41280c do not have complex multiplication.Modular form 41280.2.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.