Properties

Label 233450cg
Number of curves $2$
Conductor $233450$
CM no
Rank $0$
Graph

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

Elliptic curves in class 233450cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
233450.cg2 233450cg1 \([1, -1, 1, -1289530, 563959097]\) \(-15177411906818559273/167619938752\) \(-2619061543000000\) \([2]\) \(3538944\) \(2.1123\) \(\Gamma_0(N)\)-optimal
233450.cg1 233450cg2 \([1, -1, 1, -20632530, 36077707097]\) \(62167173500157644301993/7582456\) \(118475875000\) \([2]\) \(7077888\) \(2.4588\)  

Rank

sage: E.rank()
 

The elliptic curves in class 233450cg have rank \(0\).

Complex multiplication

The elliptic curves in class 233450cg do not have complex multiplication.

Modular form 233450.2.a.cg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 3 q^{9} + 4 q^{11} + 4 q^{13} - q^{14} + q^{16} - 3 q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.