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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 8470p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8470.p1 | 8470p1 | \([1, -1, 0, -280924, 57381968]\) | \(-11437987859001/358400\) | \(-76826222950400\) | \([]\) | \(116160\) | \(1.7606\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8470p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8470p do not have complex multiplication.Modular form 8470.2.a.p
sage: E.q_eigenform(10)