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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4704x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.p1 | 4704x1 | \([0, -1, 0, 19, -27]\) | \(3584/3\) | \(-602112\) | \([]\) | \(960\) | \(-0.20329\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4704x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4704x do not have complex multiplication.Modular form 4704.2.a.x
sage: E.q_eigenform(10)