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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 499257.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
499257.a1 | 499257a1 | \([0, 0, 1, -136161, 20004320]\) | \(-2985984/121\) | \(-11313052514847963\) | \([]\) | \(5034240\) | \(1.8482\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 499257.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 499257.a do not have complex multiplication.Modular form 499257.2.a.a
sage: E.q_eigenform(10)