Properties

Label 5390.bh
Number of curves $4$
Conductor $5390$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5390.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5390.bh1 5390x4 \([1, 1, 1, -172481, 27349153]\) \(4823468134087681/30382271150\) \(3574443818526350\) \([2]\) \(55296\) \(1.8218\)  
5390.bh2 5390x2 \([1, 1, 1, -13231, -566147]\) \(2177286259681/105875000\) \(12456087875000\) \([2]\) \(18432\) \(1.2725\)  
5390.bh3 5390x3 \([1, 1, 1, -4411, 928549]\) \(-80677568161/3131816380\) \(-368455065290620\) \([2]\) \(27648\) \(1.4752\)  
5390.bh4 5390x1 \([1, 1, 1, 489, -33811]\) \(109902239/4312000\) \(-507302488000\) \([2]\) \(9216\) \(0.92589\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5390.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 5390.bh do not have complex multiplication.

Modular form 5390.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} + q^{8} + q^{9} - q^{10} - q^{11} + 2q^{12} - 2q^{13} - 2q^{15} + q^{16} - 6q^{17} + q^{18} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.