Properties

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

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 40310.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.bb1 40310z1 \([1, 1, 1, -23205, 4618475]\) \(-1381877673393082321/8453619712000000\) \(-8453619712000000\) \([]\) \(336960\) \(1.7398\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310.bb1 has rank \(1\).

Complex multiplication

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

Modular form 40310.2.a.bb

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