Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("100800.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800mh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.q3 100800mh1 [0, 0, 0, -17860575, -29053019000] [2] 2949120 \(\Gamma_0(N)\)-optimal
100800.q2 100800mh2 [0, 0, 0, -17861700, -29049176000] [2, 2] 5898240  
100800.q4 100800mh3 [0, 0, 0, -15674700, -36428114000] [2] 11796480  
100800.q1 100800mh4 [0, 0, 0, -20066700, -21424286000] [2] 11796480  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.q

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

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.