Properties

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

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 112710be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112710.w1 112710be1 \([1, 0, 1, -1749, 113272]\) \(-2045682844201/18044839800\) \(-5214958702200\) \([]\) \(280800\) \(1.1228\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 112710be1 has rank \(1\).

Complex multiplication

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

Modular form 112710.2.a.be

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