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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 111573.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111573.e1 | 111573ba1 | \([0, 0, 1, -399, 3064]\) | \(196661248/253\) | \(9037413\) | \([]\) | \(38160\) | \(0.24237\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 111573.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 111573.e do not have complex multiplication.Modular form 111573.2.a.e
sage: E.q_eigenform(10)