Properties

Label 1008.i
Number of curves $2$
Conductor $1008$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1008.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1008.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1008.i1 1008a1 [0, 0, 0, -54, 135] [2] 192 \(\Gamma_0(N)\)-optimal
1008.i2 1008a2 [0, 0, 0, 81, 702] [2] 384  

Rank

sage: E.rank()
 

The elliptic curves in class 1008.i have rank \(1\).

Modular form 1008.2.a.i

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{7} - 6q^{11} - 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.