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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 19890.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19890.a1 | 19890j1 | \([1, -1, 0, -12690, -547700]\) | \(-310027558782241/414375000\) | \(-302079375000\) | \([]\) | \(64512\) | \(1.1088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19890.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19890.a do not have complex multiplication.Modular form 19890.2.a.a
sage: E.q_eigenform(10)