Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3136.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3136.a1 3136bc1 [0, 0, 0, -28, -56] [] 384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3136.a1 has rank \(1\).

Complex multiplication

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

Modular form 3136.2.a.a

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