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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 85176bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.s1 | 85176bd1 | \([0, 0, 0, -58181331, -42237375154]\) | \(86323786849188610514/46901442470561469\) | \(11833967849094437974566912\) | \([]\) | \(12082176\) | \(3.5020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 85176bd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 85176bd do not have complex multiplication.Modular form 85176.2.a.bd
sage: E.q_eigenform(10)