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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 139650.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.bf1 | 139650jp1 | \([1, 1, 0, -9825, 392085]\) | \(-727890625/49248\) | \(-7097622991200\) | \([]\) | \(403200\) | \(1.2175\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139650.bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 139650.bf do not have complex multiplication.Modular form 139650.2.a.bf
sage: E.q_eigenform(10)