Properties

Label 2100.a
Number of curves $4$
Conductor $2100$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2100.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2100.a1 2100c4 \([0, -1, 0, -45708, -3746088]\) \(2640279346000/3087\) \(12348000000\) \([2]\) \(5184\) \(1.2195\)  
2100.a2 2100c3 \([0, -1, 0, -2833, -58838]\) \(-10061824000/352947\) \(-88236750000\) \([2]\) \(2592\) \(0.87295\)  
2100.a3 2100c2 \([0, -1, 0, -708, -2088]\) \(9826000/5103\) \(20412000000\) \([2]\) \(1728\) \(0.67022\)  
2100.a4 2100c1 \([0, -1, 0, 167, -338]\) \(2048000/1323\) \(-330750000\) \([2]\) \(864\) \(0.32365\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2100.a have rank \(0\).

Complex multiplication

The elliptic curves in class 2100.a do not have complex multiplication.

Modular form 2100.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 6 q^{11} - 2 q^{13} - 4 q^{19} + O(q^{20})\) Copy content 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 LMFDB 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 LMFDB labels.