Properties

Label 100800d
Number of curves $4$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100800.ee1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.ee2 100800d1 [0, 0, 0, -168300, 26542000] [2] 442368 \(\Gamma_0(N)\)-optimal
100800.ee3 100800d2 [0, 0, 0, -120300, 41998000] [2] 884736  
100800.ee1 100800d3 [0, 0, 0, -672300, -185922000] [2] 1327104  
100800.ee4 100800d4 [0, 0, 0, 1055700, -984258000] [2] 2654208  

Rank

sage: E.rank()
 

The elliptic curves in class 100800d have rank \(1\).

Modular form 100800.2.a.ee

sage: E.q_eigenform(10)
 
\( q - q^{7} + 2q^{13} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.