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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7623k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7623.d1 | 7623k1 | \([0, 0, 1, -1625151, 726460798]\) | \(25104437248/2470629\) | \(46715598231912597141\) | \([]\) | \(354816\) | \(2.5111\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7623k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 7623k do not have complex multiplication.Modular form 7623.2.a.k
sage: E.q_eigenform(10)