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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 7623a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7623.p1 | 7623a1 | \([0, 0, 1, -3993, -69545]\) | \(1216512/343\) | \(1985177596941\) | \([]\) | \(12672\) | \(1.0666\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7623a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 7623a do not have complex multiplication.Modular form 7623.2.a.a
sage: E.q_eigenform(10)