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SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 450800ec
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450800.ec1 | 450800ec1 | \([0, 0, 0, 18038125, 7072231250]\) | \(137927116575/84410368\) | \(-397231815393280000000000\) | \([]\) | \(42024960\) | \(3.2174\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450800ec1 has rank \(1\).
Complex multiplication
The elliptic curves in class 450800ec do not have complex multiplication.Modular form 450800.2.a.ec
sage: E.q_eigenform(10)