Properties

Label 327990.bl
Number of curves $4$
Conductor $327990$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bl1 327990bl4 \([1, 0, 0, -406641, -99824049]\) \(12501706118329/2570490\) \(1528987398397290\) \([2]\) \(2867200\) \(1.9107\)  
327990.bl2 327990bl2 \([1, 0, 0, -28191, -1199979]\) \(4165509529/1368900\) \(814253644116900\) \([2, 2]\) \(1433600\) \(1.5641\)  
327990.bl3 327990bl1 \([1, 0, 0, -11371, 451745]\) \(273359449/9360\) \(5567546284560\) \([2]\) \(716800\) \(1.2175\) \(\Gamma_0(N)\)-optimal
327990.bl4 327990bl3 \([1, 0, 0, 81139, -8218965]\) \(99317171591/106616250\) \(-63417831897566250\) \([2]\) \(2867200\) \(1.9107\)  

Rank

sage: E.rank()
 

The elliptic curves in class 327990.bl have rank \(1\).

Complex multiplication

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

Modular form 327990.2.a.bl

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