Properties

Label 40310.r
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 40310.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.r1 40310q1 \([1, 1, 1, -68183196, -219331472771]\) \(-35055468499828627267048916929/489806610720610058240000\) \(-489806610720610058240000\) \([]\) \(6323200\) \(3.3517\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 40310.2.a.r

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