Properties

Label 327990.y
Number of curves $4$
Conductor $327990$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.y1 327990y4 \([1, 1, 1, -274211011, -1747842838417]\) \(3833455222908263170009/14910644531250\) \(8869199098328613281250\) \([2]\) \(51609600\) \(3.4245\)  
327990.y2 327990y2 \([1, 1, 1, -17394841, -26455414141]\) \(978581759592931129/58281773062500\) \(34667357806804590562500\) \([2, 2]\) \(25804800\) \(3.0779\)  
327990.y3 327990y1 \([1, 1, 1, -3249221, 1739635643]\) \(6377838054073849/1489533786000\) \(886009433330223306000\) \([2]\) \(12902400\) \(2.7313\) \(\Gamma_0(N)\)-optimal
327990.y4 327990y3 \([1, 1, 1, 13091409, -109268263641]\) \(417152543917888871/8913566138987250\) \(-5301997012745543621657250\) \([2]\) \(51609600\) \(3.4245\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990.y have rank \(0\).

Complex multiplication

The elliptic curves in class 327990.y do not have complex multiplication.

Modular form 327990.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - q^{12} - q^{13} + q^{15} + q^{16} + 2q^{17} + q^{18} + O(q^{20})\)  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.