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Properties

Label 424830.do
Number of curves $2$
Conductor $424830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 424830.do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.do1 424830do2 \([1, 0, 1, -5822609903, 171010750626146]\) \(37769548376817211811066153/1011738331054080\) \(584794404297721502760960\) \([2]\) \(424673280\) \(4.0740\) \(\Gamma_0(N)\)-optimal*
424830.do2 424830do1 \([1, 0, 1, -363461103, 2678989207906]\) \(-9186763300983704416553/47730830553907200\) \(-27588875269089354212966400\) \([2]\) \(212336640\) \(3.7274\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 424830.do1.

Rank

sage: E.rank()
 

The elliptic curves in class 424830.do have rank \(0\).

Complex multiplication

The elliptic curves in class 424830.do do not have complex multiplication.

Modular form 424830.2.a.do

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} - 6 q^{11} + q^{12} + 4 q^{13} + q^{15} + q^{16} - q^{18} + O(q^{20})\) 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.