Properties

Label 450800gh
Number of curves $2$
Conductor $450800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gh1")
 
E.isogeny_class()
 

Elliptic curves in class 450800gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450800.gh2 450800gh1 \([0, -1, 0, -178752408, 881629955312]\) \(83890194895342081/3958384640000\) \(29804799648727040000000000\) \([2]\) \(123863040\) \(3.6488\) \(\Gamma_0(N)\)-optimal
450800.gh1 450800gh2 \([0, -1, 0, -492352408, -3057186044688]\) \(1753007192038126081/478174101507200\) \(3600429111566116659200000000\) \([2]\) \(247726080\) \(3.9954\)  

Rank

sage: E.rank()
 

The elliptic curves in class 450800gh have rank \(0\).

Complex multiplication

The elliptic curves in class 450800gh do not have complex multiplication.

Modular form 450800.2.a.gh

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{9} + 2 q^{11} - 4 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.