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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 439569.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 439569.f1 | 439569f1 | \([0, 0, 1, -1904799, 1025575528]\) | \(-15388672/243\) | \(-12069139467005107227\) | \([]\) | \(13590720\) | \(2.4628\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 439569.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 439569.f do not have complex multiplication.Modular form 439569.2.a.f
sage: E.q_eigenform(10)