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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 134640.dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134640.dk1 | 134640h1 | \([0, 0, 0, -10678641627, 424773922697354]\) | \(-45100802713464654722769650329/4293192974400000000000\) | \(-12819405530470809600000000000\) | \([]\) | \(129254400\) | \(4.4302\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 134640.dk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 134640.dk do not have complex multiplication.Modular form 134640.2.a.dk
sage: E.q_eigenform(10)