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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 49686bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.bp1 | 49686bl1 | \([1, 0, 1, -832108177, 9291628742372]\) | \(-112205650221491190337/745029571313664\) | \(-423079385410317245483188224\) | \([]\) | \(38384640\) | \(3.9447\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49686bl1 has rank \(1\).
Complex multiplication
The elliptic curves in class 49686bl do not have complex multiplication.Modular form 49686.2.a.bl
sage: E.q_eigenform(10)