Properties

Label 104742.i
Number of curves $1$
Conductor $104742$
CM no
Rank $0$

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

Elliptic curves in class 104742.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
104742.i1 104742z1 \([1, -1, 0, 10788327, 15502654341]\) \(105756712489/140300424\) \(-184220109445058785667448\) \([]\) \(12400128\) \(3.1500\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 104742.i1 has rank \(0\).

Complex multiplication

The elliptic curves in class 104742.i do not have complex multiplication.

Modular form 104742.2.a.i

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