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Properties

Label 458640j
Number of curves $1$
Conductor $458640$
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 458640j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 458640j do not have complex multiplication.

Modular form 458640.2.a.j

Copy content sage:E.q_eigenform(10)
 
\(q - q^{5} - 5 q^{11} - q^{13} + 3 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 458640j

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.j1 458640j1 \([0, 0, 0, 4285932, -2247416948]\) \(396555344454656/328867205355\) \(-7220650119016647156480\) \([]\) \(31933440\) \(2.8820\) \(\Gamma_0(N)\)-optimal