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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 7623.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7623.a1 | 7623s1 | \([0, 0, 1, -762663, -255481790]\) | \(313944395776/1240029\) | \(193776385829863221\) | \([]\) | \(185856\) | \(2.1744\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7623.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 7623.a do not have complex multiplication.Modular form 7623.2.a.a
sage: E.q_eigenform(10)