Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 40310.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.i1 40310j1 \([1, 1, 0, -6609627, -6543551459]\) \(-31934099190271784872597561/1456024407611801600\) \(-1456024407611801600\) \([]\) \(1175040\) \(2.5611\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310.i1 has rank \(1\).

Complex multiplication

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

Modular form 40310.2.a.i

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