Properties

Label 129285.i
Number of curves $1$
Conductor $129285$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 129285.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129285.i1 129285c1 \([0, 0, 1, -10978578, -22653288421]\) \(-1540318675894272/1442042265625\) \(-137002785082189384921875\) \([]\) \(10725120\) \(3.1360\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 129285.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 129285.i do not have complex multiplication.

Modular form 129285.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} - 4 q^{7} - 2 q^{11} + 4 q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display