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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 174570.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 174570.bc1 | 174570cd1 | \([1, 0, 1, -530395709, 4873550214296]\) | \(-1356251428305237257849552687/58465103838953017536000\) | \(-711344918408541364360512000\) | \([]\) | \(137168640\) | \(3.9182\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 174570.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 174570.bc do not have complex multiplication.Modular form 174570.2.a.bc
sage: E.q_eigenform(10)