Properties

Label 222768cg
Number of curves $1$
Conductor $222768$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 222768cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222768.fy1 222768cg1 \([0, 0, 0, -419376, -104533648]\) \(-2731787761881088/19171971\) \(-57247198654464\) \([]\) \(1320960\) \(1.8192\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 222768cg1 has rank \(1\).

Complex multiplication

The elliptic curves in class 222768cg do not have complex multiplication.

Modular form 222768.2.a.cg

sage: E.q_eigenform(10)
 
\(q + 3 q^{5} + q^{7} + 2 q^{11} + q^{13} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display