Properties

Label 40310.q
Number of curves $1$
Conductor $40310$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 40310.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.q1 40310ba1 \([1, 0, 0, -220, -240]\) \(1177918188481/660439040\) \(660439040\) \([]\) \(20880\) \(0.38255\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40310.q do not have complex multiplication.

Modular form 40310.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} + q^{5} - 2 q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} - 2 q^{12} + 3 q^{13} + q^{14} - 2 q^{15} + q^{16} - 6 q^{17} + q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display