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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 272734.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272734.bc1 | 272734bc1 | \([1, -1, 0, 112107385, 16433727529533]\) | \(18013683824433/13497989595136\) | \(-116759689239497813040207757312\) | \([]\) | \(409812480\) | \(4.2565\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 272734.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 272734.bc do not have complex multiplication.Modular form 272734.2.a.bc
sage: E.q_eigenform(10)