Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.g3 3360f1 \([0, -1, 0, -5250, -144648]\) \(250094631024064/62015625\) \(3969000000\) \([2, 2]\) \(3072\) \(0.82939\) \(\Gamma_0(N)\)-optimal
3360.g1 3360f2 \([0, -1, 0, -84000, -9342648]\) \(128025588102048008/7875\) \(4032000\) \([2]\) \(6144\) \(1.1760\)  
3360.g2 3360f3 \([0, -1, 0, -5880, -107100]\) \(43919722445768/15380859375\) \(7875000000000\) \([4]\) \(6144\) \(1.1760\)  
3360.g4 3360f4 \([0, -1, 0, -4625, -181023]\) \(-2671731885376/1969120125\) \(-8065516032000\) \([2]\) \(6144\) \(1.1760\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3360.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 2q^{17} + 8q^{19} + O(q^{20})\)  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.