Properties

Label 112710bu
Number of curves $1$
Conductor $112710$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 112710bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112710.by1 112710bu1 \([1, 1, 1, -124276, 93553349]\) \(-2541499591834369/43848960714000\) \(-3662309047793994000\) \([]\) \(3110400\) \(2.2432\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 112710bu1 has rank \(1\).

Complex multiplication

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

Modular form 112710.2.a.bu

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