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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 121242bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121242.bd1 | 121242bd1 | \([1, 1, 1, 18329, 3073181]\) | \(3176852591/20777472\) | \(-4453835647928832\) | \([]\) | \(1378080\) | \(1.6845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121242bd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 121242bd do not have complex multiplication.Modular form 121242.2.a.bd
sage: E.q_eigenform(10)