Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.u1 3360m3 \([0, 1, 0, -680, 6600]\) \(68017239368/39375\) \(20160000\) \([4]\) \(1024\) \(0.34719\)  
3360.u2 3360m2 \([0, 1, 0, -400, -3172]\) \(13858588808/229635\) \(117573120\) \([2]\) \(1024\) \(0.34719\)  
3360.u3 3360m1 \([0, 1, 0, -50, 48]\) \(220348864/99225\) \(6350400\) \([2, 2]\) \(512\) \(0.00061629\) \(\Gamma_0(N)\)-optimal
3360.u4 3360m4 \([0, 1, 0, 175, 543]\) \(143877824/108045\) \(-442552320\) \([2]\) \(1024\) \(0.34719\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3360.2.a.u

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.