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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 102550.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102550.p1 | 102550k1 | \([1, 1, 0, -875, -12625]\) | \(-4750104241/1406986\) | \(-21984156250\) | \([]\) | \(94080\) | \(0.69886\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 102550.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 102550.p do not have complex multiplication.Modular form 102550.2.a.p
sage: E.q_eigenform(10)