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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 61347.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61347.bc1 | 61347n1 | \([0, -1, 1, -63357818, -195744331729]\) | \(-160855552000/1594323\) | \(-278781924031337757667923\) | \([]\) | \(9904752\) | \(3.3181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61347.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 61347.bc do not have complex multiplication.Modular form 61347.2.a.bc
sage: E.q_eigenform(10)