Properties

Label 123200.hg
Number of curves $2$
Conductor $123200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("hg1")
 
E.isogeny_class()
 

Elliptic curves in class 123200.hg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123200.hg1 123200bp2 \([0, -1, 0, -82433, 8436737]\) \(15124197817/1294139\) \(5300793344000000\) \([2]\) \(786432\) \(1.7584\)  
123200.hg2 123200bp1 \([0, -1, 0, 5567, 604737]\) \(4657463/41503\) \(-169996288000000\) \([2]\) \(393216\) \(1.4118\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 123200.hg have rank \(0\).

Complex multiplication

The elliptic curves in class 123200.hg do not have complex multiplication.

Modular form 123200.2.a.hg

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{7} + q^{9} - q^{11} + 4 q^{13} - 4 q^{17} + O(q^{20})\) 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 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.