Properties

Label 112710k
Number of curves $1$
Conductor $112710$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 112710k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112710.l1 112710k1 \([1, 1, 0, 30310748, 49525284016]\) \(127591024063258622231/117712954934172000\) \(-2841304571917467107868000\) \([]\) \(35942400\) \(3.3795\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 112710k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 112710k do not have complex multiplication.

Modular form 112710.2.a.k

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