Properties

Label 3360.j
Number of curves $2$
Conductor $3360$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.j1 3360h1 \([0, -1, 0, -210, -900]\) \(16079333824/2953125\) \(189000000\) \([2]\) \(1152\) \(0.30659\) \(\Gamma_0(N)\)-optimal
3360.j2 3360h2 \([0, -1, 0, 415, -5775]\) \(1925134784/4465125\) \(-18289152000\) \([2]\) \(2304\) \(0.65316\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3360.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.