Properties

Label 40362.f
Number of curves $1$
Conductor $40362$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 40362.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40362.f1 40362a1 \([1, 1, 0, 13605, -7334883]\) \(289765104938375/24390120480768\) \(-23438905782018048\) \([]\) \(257400\) \(1.8206\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40362.f1 has rank \(0\).

Complex multiplication

The elliptic curves in class 40362.f do not have complex multiplication.

Modular form 40362.2.a.f

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