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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 111573.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111573.a1 | 111573bb1 | \([0, 0, 1, -71589, -208435698]\) | \(-473093337088/218558899251\) | \(-18744948998788075371\) | \([]\) | \(2949120\) | \(2.3772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 111573.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 111573.a do not have complex multiplication.Modular form 111573.2.a.a
sage: E.q_eigenform(10)