Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 112710cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112710.cr1 112710cm1 \([1, 0, 0, -1281, 18765]\) \(-804441463921/66832740\) \(-19314661860\) \([]\) \(120960\) \(0.71921\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 112710cm1 has rank \(1\).

Complex multiplication

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

Modular form 112710.2.a.cm

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