Properties

Label 3136.b
Number of curves $1$
Conductor $3136$
CM no
Rank $1$

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

Elliptic curves in class 3136.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3136.b1 3136c1 [0, 0, 0, -1372, -19208] [] 2688 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3136.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3136.b do not have complex multiplication.

Modular form 3136.2.a.b

sage: E.q_eigenform(10)
 
\( q - 3q^{3} + q^{5} + 6q^{9} + q^{11} - 2q^{13} - 3q^{15} + 3q^{17} - 5q^{19} + O(q^{20}) \)