Properties

Label 3380.c
Number of curves 4
Conductor 3380
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("3380.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3380.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3380.c1 3380i3 [0, 1, 0, -6985, -226992] [2] 3456  
3380.c2 3380i4 [0, 1, 0, -6140, -283100] [2] 6912  
3380.c3 3380i1 [0, 1, 0, -225, 820] [2] 1152 \(\Gamma_0(N)\)-optimal
3380.c4 3380i2 [0, 1, 0, 620, 6228] [2] 2304  

Rank

sage: E.rank()
 

The elliptic curves in class 3380.c have rank \(1\).

Modular form 3380.2.a.c

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} - 2q^{7} + q^{9} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.