Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("100800.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800md

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.u3 100800md1 [0, 0, 0, -284700, -58466000] [2] 589824 \(\Gamma_0(N)\)-optimal
100800.u2 100800md2 [0, 0, 0, -302700, -50654000] [2, 2] 1179648  
100800.u4 100800md3 [0, 0, 0, 669300, -309206000] [2] 2359296  
100800.u1 100800md4 [0, 0, 0, -1562700, 707866000] [2] 2359296  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.u

sage: E.q_eigenform(10)
 
\( q - q^{7} - 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.