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SageMath
E = EllipticCurve("gk1")
E.isogeny_class()
Elliptic curves in class 253575.gk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253575.gk1 | 253575gk1 | \([0, 0, 1, -1062075, -491615469]\) | \(-98867482624/20696067\) | \(-27734709164782921875\) | \([]\) | \(9216000\) | \(2.4525\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 253575.gk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 253575.gk do not have complex multiplication.Modular form 253575.2.a.gk
sage: E.q_eigenform(10)