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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 169400cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169400.cc1 | 169400cd1 | \([0, 0, 0, -1246300, -551699500]\) | \(-30211716096/1071875\) | \(-7595567787500000000\) | \([]\) | \(6854400\) | \(2.3951\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169400cd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 169400cd do not have complex multiplication.Modular form 169400.2.a.cd
sage: E.q_eigenform(10)