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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 30345.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30345.p1 | 30345w1 | \([0, 1, 1, -10211, 583745]\) | \(-4878401536/3346875\) | \(-80785426246875\) | \([]\) | \(69120\) | \(1.3689\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 30345.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 30345.p do not have complex multiplication.Modular form 30345.2.a.p
sage: E.q_eigenform(10)