Properties

Label 104742p
Number of curves $1$
Conductor $104742$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 104742p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
104742.c1 104742p1 \([1, -1, 0, -858679776, 9646255952896]\) \(648817971720191270353/3006677182316544\) \(324475078493158364756312064\) \([]\) \(77045760\) \(3.9374\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 104742p1 has rank \(1\).

Complex multiplication

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

Modular form 104742.2.a.p

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