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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 41650x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.m1 | 41650x1 | \([1, 1, 0, 1662300, 134644000]\) | \(11053587253415/6565418768\) | \(-301724590873606250000\) | \([]\) | \(1572480\) | \(2.6190\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 41650x do not have complex multiplication.Modular form 41650.2.a.x
sage: E.q_eigenform(10)