Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 40310.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.b1 40310o1 \([1, 1, 0, -217, 2069]\) \(-1138220196121/1356028400\) \(-1356028400\) \([]\) \(25344\) \(0.44618\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310.b1 has rank \(2\).

Complex multiplication

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

Modular form 40310.2.a.b

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