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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 7623.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7623.e1 | 7623h1 | \([1, -1, 1, -3506603, 2534429868]\) | \(-30515071121161/85766121\) | \(-13402467969722268129\) | \([]\) | \(228096\) | \(2.5425\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7623.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 7623.e do not have complex multiplication.Modular form 7623.2.a.e
sage: E.q_eigenform(10)