Properties

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

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

Elliptic curves in class 3136a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3136.u1 3136a1 \([0, 1, 0, -65, 167]\) \(12544\) \(2458624\) \([]\) \(384\) \(-0.030300\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3136.2.a.a

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