Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.i3 3360p1 \([0, -1, 0, -70, -200]\) \(601211584/11025\) \(705600\) \([2, 2]\) \(768\) \(-0.082988\) \(\Gamma_0(N)\)-optimal
3360.i1 3360p2 \([0, -1, 0, -1120, -14060]\) \(303735479048/105\) \(53760\) \([2]\) \(1536\) \(0.26359\)  
3360.i2 3360p3 \([0, -1, 0, -145, 385]\) \(82881856/36015\) \(147517440\) \([4]\) \(1536\) \(0.26359\)  
3360.i4 3360p4 \([0, -1, 0, 0, -648]\) \(-8/354375\) \(-181440000\) \([2]\) \(1536\) \(0.26359\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3360.2.a.p

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