Properties

Label 3360o
Number of curves $4$
Conductor $3360$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.l3 3360o1 \([0, -1, 0, -50, -48]\) \(220348864/99225\) \(6350400\) \([2, 2]\) \(512\) \(0.00061629\) \(\Gamma_0(N)\)-optimal
3360.l1 3360o2 \([0, -1, 0, -680, -6600]\) \(68017239368/39375\) \(20160000\) \([2]\) \(1024\) \(0.34719\)  
3360.l2 3360o3 \([0, -1, 0, -400, 3172]\) \(13858588808/229635\) \(117573120\) \([2]\) \(1024\) \(0.34719\)  
3360.l4 3360o4 \([0, -1, 0, 175, -543]\) \(143877824/108045\) \(-442552320\) \([4]\) \(1024\) \(0.34719\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3360o have rank \(0\).

Complex multiplication

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

Modular form 3360.2.a.o

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