Properties

Label 122694.z
Number of curves $1$
Conductor $122694$
CM no
Rank $1$

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

Elliptic curves in class 122694.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122694.z1 122694k1 \([1, 1, 0, -4340261, -3484541133]\) \(-1407450852604763/1119214746\) \(-7190375861679859134\) \([]\) \(5419008\) \(2.5486\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 122694.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 122694.z do not have complex multiplication.

Modular form 122694.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} + 3 q^{7} - q^{8} + q^{9} - 3 q^{10} - q^{12} - 3 q^{14} - 3 q^{15} + q^{16} - 2 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display