Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.n3 3360i1 \([0, 1, 0, -4326, -90576]\) \(139927692143296/27348890625\) \(1750329000000\) \([2, 2]\) \(4608\) \(1.0660\) \(\Gamma_0(N)\)-optimal
3360.n1 3360i2 \([0, 1, 0, -65576, -6485076]\) \(60910917333827912/3255076125\) \(1666598976000\) \([2]\) \(9216\) \(1.4126\)  
3360.n2 3360i3 \([0, 1, 0, -21201, 1100799]\) \(257307998572864/19456203375\) \(79692609024000\) \([2]\) \(9216\) \(1.4126\)  
3360.n4 3360i4 \([0, 1, 0, 8904, -524520]\) \(152461584507448/322998046875\) \(-165375000000000\) \([2]\) \(9216\) \(1.4126\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3360.2.a.i

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 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.