Properties

Label 116242s
Number of curves $1$
Conductor $116242$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 116242s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116242.u1 116242s1 \([1, 0, 0, -582481, 139784329]\) \(464566023349849/89298034336\) \(4201104696905370016\) \([]\) \(1728000\) \(2.2907\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 116242s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 116242s do not have complex multiplication.

Modular form 116242.2.a.s

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