Properties

Label 109956.z
Number of curves $1$
Conductor $109956$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 109956.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
109956.z1 109956bc1 \([0, 1, 0, -111589, 585539975]\) \(-5102271397888/4915446963867\) \(-148044139482109102848\) \([]\) \(3773952\) \(2.5494\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 109956.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 109956.z do not have complex multiplication.

Modular form 109956.2.a.z

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