Properties

Label 188760.cg
Number of curves $2$
Conductor $188760$
CM no
Rank $0$
Graph

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

Elliptic curves in class 188760.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.cg1 188760bq2 \([0, 1, 0, -99829880, -271404080400]\) \(22784591413352662/6597644551875\) \(31860532709647126467840000\) \([2]\) \(72382464\) \(3.5998\)  
188760.cg2 188760bq1 \([0, 1, 0, 16606000, -28099665552]\) \(209741642018356/262704572325\) \(-634310287082369281612800\) \([2]\) \(36191232\) \(3.2533\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 188760.cg have rank \(0\).

Complex multiplication

The elliptic curves in class 188760.cg do not have complex multiplication.

Modular form 188760.2.a.cg

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 4q^{7} + q^{9} + q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.