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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 52416dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52416.u1 | 52416dk1 | \([0, 0, 0, -4044, 214576]\) | \(-306182024/655473\) | \(-15657855123456\) | \([]\) | \(112640\) | \(1.2207\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 52416dk1 has rank \(2\).
Complex multiplication
The elliptic curves in class 52416dk do not have complex multiplication.Modular form 52416.2.a.dk
sage: E.q_eigenform(10)