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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 135240.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135240.bc1 | 135240dk1 | \([0, -1, 0, -247760, -78726948]\) | \(-284927760964/289635435\) | \(-1709763220811197440\) | \([]\) | \(2338560\) | \(2.1941\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 135240.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 135240.bc do not have complex multiplication.Modular form 135240.2.a.bc
sage: E.q_eigenform(10)