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SageMath
E = EllipticCurve("lp1")
E.isogeny_class()
Elliptic curves in class 487872.lp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487872.lp1 | 487872lp1 | \([0, 0, 0, -7232412, 7753884248]\) | \(-31636584484096/1331669031\) | \(-1761083288418066471936\) | \([]\) | \(22118400\) | \(2.8433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872.lp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 487872.lp do not have complex multiplication.Modular form 487872.2.a.lp
sage: E.q_eigenform(10)