Properties

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

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

Elliptic curves in class 1083d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1083.b2 1083d1 \([1, 0, 0, 2, -1]\) \(2375/3\) \(-1083\) \([]\) \(36\) \(-0.73170\) \(\Gamma_0(N)\)-optimal
1083.b1 1083d2 \([1, 0, 0, -663, 6516]\) \(-89289015625/2187\) \(-789507\) \([]\) \(252\) \(0.24125\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1083.2.a.d

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 Cremona 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 Cremona labels.