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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 304200.fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304200.fa1 | 304200fa1 | \([0, 0, 0, -32955, -2570490]\) | \(-7020\) | \(-563833074355200\) | \([]\) | \(1138176\) | \(1.5614\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 304200.fa1 has rank \(1\).
Complex multiplication
The elliptic curves in class 304200.fa do not have complex multiplication.Modular form 304200.2.a.fa
sage: E.q_eigenform(10)