Properties

Label 100800.a
Number of curves 2
Conductor 100800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100800.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.a1 100800hj2 [0, 0, 0, -124500, -16900000] [2] 655360  
100800.a2 100800hj1 [0, 0, 0, -6375, -362500] [2] 327680 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{7} - 6q^{11} - 6q^{13} + 2q^{19} + O(q^{20}) \)

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 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.