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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 409101.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.a1 | 409101a1 | \([0, -1, 1, -571160, -193688188]\) | \(-98867482624/20696067\) | \(-4313523542621409963\) | \([]\) | \(17136000\) | \(2.2974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 409101.a do not have complex multiplication.Modular form 409101.2.a.a
sage: E.q_eigenform(10)