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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 84150df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.bb1 | 84150df1 | \([1, -1, 0, -44757117, 282512307541]\) | \(-6963898974088537853/20183964977485584\) | \(-28738497008958966281250000\) | \([]\) | \(17971200\) | \(3.5720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 84150df1 has rank \(0\).
Complex multiplication
The elliptic curves in class 84150df do not have complex multiplication.Modular form 84150.2.a.df
sage: E.q_eigenform(10)