Properties

Label 253575.gk
Number of curves $1$
Conductor $253575$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("gk1")
 
E.isogeny_class()
 

Elliptic curves in class 253575.gk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
253575.gk1 253575gk1 \([0, 0, 1, -1062075, -491615469]\) \(-98867482624/20696067\) \(-27734709164782921875\) \([]\) \(9216000\) \(2.4525\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 253575.gk1 has rank \(1\).

Complex multiplication

The elliptic curves in class 253575.gk do not have complex multiplication.

Modular form 253575.2.a.gk

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 5 q^{11} - 2 q^{13} - 4 q^{16} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display