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Properties

Label 458913j
Number of curves $1$
Conductor $458913$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("j1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 458913j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 458913j do not have complex multiplication.

Modular form 458913.2.a.j

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

Elliptic curves in class 458913j

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458913.j1 458913j1 \([0, -1, 1, 4269180, -10910193631]\) \(1811564780171264/11870974573731\) \(-56388366667482790293171\) \([]\) \(47308800\) \(3.0473\) \(\Gamma_0(N)\)-optimal