Properties

Label 718b
Number of curves $1$
Conductor $718$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 718b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
718.a1 718b1 \([1, 0, 1, -5, 0]\) \(10218313/5744\) \(5744\) \([]\) \(112\) \(-0.58855\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 718b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 718b do not have complex multiplication.

Modular form 718.2.a.b

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