Properties

Label 112632u
Number of curves $1$
Conductor $112632$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 112632u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112632.z1 112632u1 \([0, 1, 0, -3116272, 2828500448]\) \(-5064278294/2302911\) \(-1521911907901306202112\) \([]\) \(5216640\) \(2.7711\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 112632u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 112632u do not have complex multiplication.

Modular form 112632.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} - 3 q^{7} + q^{9} - 3 q^{11} - q^{13} + 2 q^{15} + O(q^{20})\) Copy content Toggle raw display