Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 40310f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.l1 40310f1 \([1, 0, 1, -3548, 81178]\) \(-4937402992298041/10319360000\) \(-10319360000\) \([]\) \(41472\) \(0.80695\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310f1 has rank \(2\).

Complex multiplication

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

Modular form 40310.2.a.f

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