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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 193550.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193550.ca1 | 193550p1 | \([1, 1, 1, -4313, -104469]\) | \(4826809/316\) | \(580891937500\) | \([]\) | \(369600\) | \(1.0071\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193550.ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 193550.ca do not have complex multiplication.Modular form 193550.2.a.ca
sage: E.q_eigenform(10)