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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 58835k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58835.h1 | 58835k1 | \([0, 0, 1, -137842, 20486767]\) | \(-36274176/1715\) | \(-13694146767942515\) | \([]\) | \(764568\) | \(1.8591\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 58835k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 58835k do not have complex multiplication.Modular form 58835.2.a.k
sage: E.q_eigenform(10)