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Properties

Label 1083.c
Number of curves $2$
Conductor $1083$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 1083.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1083.c1 1083a2 \([1, 1, 0, -239350, -45171941]\) \(-89289015625/2187\) \(-37143052370667\) \([]\) \(4788\) \(1.7135\)  
1083.c2 1083a1 \([1, 1, 0, 715, 8292]\) \(2375/3\) \(-50950689123\) \([]\) \(684\) \(0.74052\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1083.c have rank \(1\).

Complex multiplication

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

Modular form 1083.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} + q^{7} - 3 q^{8} + q^{9} - 2 q^{11} + q^{12} + 5 q^{13} + q^{14} - q^{16} - 4 q^{17} + q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.