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SageMath
E = EllipticCurve("kc1")
E.isogeny_class()
Elliptic curves in class 242550.kc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242550.kc1 | 242550kc1 | \([1, -1, 1, -299115830, 1991760017797]\) | \(-34068278205171/10307264\) | \(-895437170473416417000000\) | \([]\) | \(54190080\) | \(3.5736\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 242550.kc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 242550.kc do not have complex multiplication.Modular form 242550.2.a.kc
sage: E.q_eigenform(10)