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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 409101.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.j1 | 409101j1 | \([1, 1, 1, -275822, -5457909346]\) | \(-1877953/10412307\) | \(-12866865638635959710067\) | \([]\) | \(22752576\) | \(2.9213\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 409101.j do not have complex multiplication.Modular form 409101.2.a.j
sage: E.q_eigenform(10)