Properties

Label 493680.j
Number of curves $1$
Conductor $493680$
CM no
Rank $1$

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

Elliptic curves in class 493680.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
493680.j1 493680j1 \([0, -1, 0, -116195856, -482245153344]\) \(-1633085171359609/734400000\) \(-78022429192087142400000\) \([]\) \(75271680\) \(3.3506\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 493680.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 493680.j do not have complex multiplication.

Modular form 493680.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 3 q^{7} + q^{9} + 3 q^{13} + q^{15} - q^{17} + O(q^{20})\) Copy content Toggle raw display