Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.e3 3360n1 \([0, -1, 0, -166, 616]\) \(7952095936/2480625\) \(158760000\) \([2, 2]\) \(1024\) \(0.27790\) \(\Gamma_0(N)\)-optimal
3360.e2 3360n2 \([0, -1, 0, -1041, -12159]\) \(30488290624/1148175\) \(4702924800\) \([2]\) \(2048\) \(0.62447\)  
3360.e1 3360n3 \([0, -1, 0, -2416, 46516]\) \(3047363673992/540225\) \(276595200\) \([4]\) \(2048\) \(0.62447\)  
3360.e4 3360n4 \([0, -1, 0, 464, 3640]\) \(21531355768/24609375\) \(-12600000000\) \([2]\) \(2048\) \(0.62447\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3360.2.a.n

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