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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 419628bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 419628.bd1 | 419628bd1 | \([0, 1, 0, -79636069, 11163845163095]\) | \(-5102271397888/4915446963867\) | \(-53808714784557794694162739968\) | \([]\) | \(557383680\) | \(4.1920\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 419628bd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 419628bd do not have complex multiplication.Modular form 419628.2.a.bd
sage: E.q_eigenform(10)