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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1309b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1309.a1 | 1309b1 | \([0, -1, 1, -22, 52]\) | \(-1231925248/155771\) | \(-155771\) | \([]\) | \(256\) | \(-0.26968\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1309b1 has rank \(2\).
Complex multiplication
The elliptic curves in class 1309b do not have complex multiplication.Modular form 1309.2.a.b
sage: E.q_eigenform(10)