Properties

Label 40310g
Number of curves $1$
Conductor $40310$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 40310g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.g1 40310g1 \([1, 1, 0, 358, 2944]\) \(5052146350679/6298437500\) \(-6298437500\) \([]\) \(21504\) \(0.56635\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310g1 has rank \(2\).

Complex multiplication

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

Modular form 40310.2.a.g

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