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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 257754.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257754.d1 | 257754d1 | \([1, 1, 0, -65638471, -204712749419]\) | \(-664779294907165541377/1884090142368\) | \(-88638680631117986208\) | \([]\) | \(26956800\) | \(3.0589\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257754.d1 has rank \(0\).
Complex multiplication
The elliptic curves in class 257754.d do not have complex multiplication.Modular form 257754.2.a.d
sage: E.q_eigenform(10)