Properties

Label 40310r
Number of curves $1$
Conductor $40310$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 40310r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.s1 40310r1 \([1, 1, 1, -2936731, -1938289431]\) \(-2801020093481184227473969/16510976000000\) \(-16510976000000\) \([]\) \(670464\) \(2.1458\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310r1 has rank \(0\).

Complex multiplication

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

Modular form 40310.2.a.r

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