Properties

Label 3360d
Number of curves $4$
Conductor $3360$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3360d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.a3 3360d1 \([0, -1, 0, -26, -24]\) \(31554496/11025\) \(705600\) \([2, 2]\) \(512\) \(-0.17631\) \(\Gamma_0(N)\)-optimal
3360.a1 3360d2 \([0, -1, 0, -376, -2684]\) \(11512557512/2835\) \(1451520\) \([2]\) \(1024\) \(0.17027\)  
3360.a2 3360d3 \([0, -1, 0, -176, 936]\) \(1184287112/36015\) \(18439680\) \([2]\) \(1024\) \(0.17027\)  
3360.a4 3360d4 \([0, -1, 0, 79, -255]\) \(13144256/13125\) \(-53760000\) \([2]\) \(1024\) \(0.17027\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3360d have rank \(1\).

Complex multiplication

The elliptic curves in class 3360d do not have complex multiplication.

Modular form 3360.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - 4q^{11} + 6q^{13} + q^{15} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.