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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 47040.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.fe1 | 47040bz1 | \([0, 1, 0, -716641, -233749825]\) | \(-215474070728/3645\) | \(-688544141967360\) | \([]\) | \(354816\) | \(1.9772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47040.fe1 has rank \(0\).
Complex multiplication
The elliptic curves in class 47040.fe do not have complex multiplication.Modular form 47040.2.a.fe
sage: E.q_eigenform(10)