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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2178.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2178.d1 | 2178e1 | \([1, -1, 0, 1611, -38219]\) | \(43307231/82944\) | \(-885285282816\) | \([]\) | \(3840\) | \(0.97703\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2178.d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2178.d do not have complex multiplication.Modular form 2178.2.a.d
sage: E.q_eigenform(10)