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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 19404.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19404.p1 | 19404y1 | \([0, 0, 0, 6027, -59339]\) | \(17643776/11319\) | \(-15532587577584\) | \([]\) | \(27648\) | \(1.2201\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19404.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19404.p do not have complex multiplication.Modular form 19404.2.a.p
sage: E.q_eigenform(10)