Properties

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

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

Elliptic curves in class 3136.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3136.b1 3136c1 \([0, 0, 0, -1372, -19208]\) \(48384\) \(5903156224\) \([]\) \(2688\) \(0.66517\) \(\Gamma_0(N)\)-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)
 
\(q - 3 q^{3} + q^{5} + 6 q^{9} + q^{11} - 2 q^{13} - 3 q^{15} + 3 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display