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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 53040.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53040.p1 | 53040bg1 | \([0, -1, 0, -3856, -94784]\) | \(-1548415333009/77332320\) | \(-316753182720\) | \([]\) | \(53760\) | \(0.96782\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53040.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 53040.p do not have complex multiplication.Modular form 53040.2.a.p
sage: E.q_eigenform(10)