Properties

Label 46800eg
Number of curves $2$
Conductor $46800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("eg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.v2 46800eg1 \([0, 0, 0, -51163635, -154318995790]\) \(-198417696411528597145/22989483914821632\) \(-1716155778447868900147200\) \([]\) \(6451200\) \(3.3865\) \(\Gamma_0(N)\)-optimal
46800.v1 46800eg2 \([0, 0, 0, -32818501875, -2288369979868750]\) \(-134057911417971280740025/1872\) \(-54587520000000000\) \([]\) \(32256000\) \(4.1912\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46800eg have rank \(0\).

Complex multiplication

The elliptic curves in class 46800eg do not have complex multiplication.

Modular form 46800.2.a.eg

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.