Properties

Label 3249.b
Number of curves $1$
Conductor $3249$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 3249.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3249.b1 3249g1 \([0, 0, 1, -7581, 279504]\) \(-1404928/171\) \(-5864692479579\) \([]\) \(11520\) \(1.1850\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3249.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3249.b do not have complex multiplication.

Modular form 3249.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{10} - q^{11} - 2 q^{13} + 10 q^{14} - 4 q^{16} + q^{17} + O(q^{20})\) Copy content Toggle raw display