Properties

Label 128122e
Number of curves $1$
Conductor $128122$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 128122e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
128122.a1 128122e1 \([1, -1, 0, -2623, -73967]\) \(-185193/116\) \(-1250388978164\) \([]\) \(401672\) \(1.0228\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 128122e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 128122e do not have complex multiplication.

Modular form 128122.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} + q^{4} + 3 q^{5} + 3 q^{6} - 2 q^{7} - q^{8} + 6 q^{9} - 3 q^{10} + q^{11} - 3 q^{12} - 3 q^{13} + 2 q^{14} - 9 q^{15} + q^{16} - 4 q^{17} - 6 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display