Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 40310.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.o1 40310e1 \([1, -1, 0, -19765, 1081781]\) \(-853938369453624489/6762895769600\) \(-6762895769600\) \([]\) \(247936\) \(1.2902\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40310.o1 has rank \(1\).

Complex multiplication

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

Modular form 40310.2.a.o

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