Properties

Label 40310n
Number of curves $1$
Conductor $40310$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 40310n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.d1 40310n1 \([1, 1, 0, -11382, 462676]\) \(-163094409140843881/103193600\) \(-103193600\) \([]\) \(35840\) \(0.85727\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310n1 has rank \(1\).

Complex multiplication

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

Modular form 40310.2.a.n

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