Properties

Label 1083.d
Number of curves $2$
Conductor $1083$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1083.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1083.d1 1083c2 \([0, -1, 1, -1584910, 768519165]\) \(-9358714467168256/22284891\) \(-1048412330083971\) \([]\) \(21600\) \(2.1236\)  
1083.d2 1083c1 \([0, -1, 1, 7100, 260625]\) \(841232384/1121931\) \(-52782232316211\) \([]\) \(4320\) \(1.3189\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1083.2.a.d

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + q^{9} + 2 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 6 q^{14} - q^{15} - 4 q^{16} + 3 q^{17} + 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.