Properties

Label 1083.a
Number of curves $4$
Conductor $1083$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1083.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1083.a1 1083b3 \([1, 1, 1, -36649, -2715724]\) \(115714886617/1539\) \(72403610859\) \([2]\) \(2160\) \(1.2272\)  
1083.a2 1083b2 \([1, 1, 1, -2354, -40714]\) \(30664297/3249\) \(152852067369\) \([2, 2]\) \(1080\) \(0.88064\)  
1083.a3 1083b1 \([1, 1, 1, -549, 4050]\) \(389017/57\) \(2681615217\) \([4]\) \(540\) \(0.53406\) \(\Gamma_0(N)\)-optimal
1083.a4 1083b4 \([1, 1, 1, 3061, -194500]\) \(67419143/390963\) \(-18393198773403\) \([2]\) \(2160\) \(1.2272\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1083.a have rank \(0\).

Complex multiplication

The elliptic curves in class 1083.a do not have complex multiplication.

Modular form 1083.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} + 3 q^{8} + q^{9} + 2 q^{10} + q^{12} - 6 q^{13} + 2 q^{15} - q^{16} - 6 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.