Properties

Label 440818.r
Number of curves $1$
Conductor $440818$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 440818.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.r1 440818r1 \([1, 1, 1, -3562, 73335]\) \(3650981477257/346358656\) \(474165000064\) \([]\) \(701568\) \(0.97838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 440818.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 440818.r do not have complex multiplication.

Modular form 440818.2.a.r

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