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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 213444.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.bd1 | 213444bb1 | \([0, 0, 0, -1138368, -516795356]\) | \(-4194304/539\) | \(-20965277243072219904\) | \([]\) | \(4147200\) | \(2.4410\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 213444.bd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 213444.bd do not have complex multiplication.Modular form 213444.2.a.bd
sage: E.q_eigenform(10)