Properties

Label 3366i
Number of curves $2$
Conductor $3366$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3366i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3366.c2 3366i1 [1, -1, 0, -108, -324] [2] 768 \(\Gamma_0(N)\)-optimal
3366.c1 3366i2 [1, -1, 0, -1638, -25110] [2] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 3366i have rank \(1\).

Complex multiplication

The elliptic curves in class 3366i do not have complex multiplication.

Modular form 3366.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{5} - 2q^{7} - q^{8} + 2q^{10} + q^{11} + 4q^{13} + 2q^{14} + q^{16} - q^{17} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.