Properties

Label 3330.w
Number of curves $4$
Conductor $3330$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3330.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.w1 3330t3 \([1, -1, 1, -3557, 82531]\) \(6825481747209/46250\) \(33716250\) \([2]\) \(2048\) \(0.62582\)  
3330.w2 3330t2 \([1, -1, 1, -227, 1279]\) \(1767172329/136900\) \(99800100\) \([2, 2]\) \(1024\) \(0.27924\)  
3330.w3 3330t1 \([1, -1, 1, -47, -89]\) \(15438249/2960\) \(2157840\) \([2]\) \(512\) \(-0.067330\) \(\Gamma_0(N)\)-optimal
3330.w4 3330t4 \([1, -1, 1, 223, 5419]\) \(1689410871/18741610\) \(-13662633690\) \([2]\) \(2048\) \(0.62582\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3330.w have rank \(0\).

Complex multiplication

The elliptic curves in class 3330.w do not have complex multiplication.

Modular form 3330.2.a.w

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.