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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 7623r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7623.s1 | 7623r1 | \([0, 0, 1, -13431, -545801]\) | \(25104437248/2470629\) | \(26369737328781\) | \([]\) | \(32256\) | \(1.3121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7623r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 7623r do not have complex multiplication.Modular form 7623.2.a.r
sage: E.q_eigenform(10)