Properties

Label 139230.eo
Number of curves $4$
Conductor $139230$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eo1")
 
E.isogeny_class()
 

Elliptic curves in class 139230.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139230.eo1 139230i4 \([1, -1, 1, -22571805272, -1305255934192629]\) \(1744596788171434949302427839201849/9588363813082031250000\) \(6989917219736800781250000\) \([2]\) \(207618048\) \(4.3812\)  
139230.eo2 139230i3 \([1, -1, 1, -1936321592, -3851550033141]\) \(1101358349464662961278219354169/628567168199833707765102000\) \(458225465617678772960759358000\) \([2]\) \(207618048\) \(4.3812\)  
139230.eo3 139230i2 \([1, -1, 1, -1411531592, -20370259905141]\) \(426646307804307769001905914169/998470877001641316000000\) \(727885269334196519364000000\) \([2, 2]\) \(103809024\) \(4.0346\)  
139230.eo4 139230i1 \([1, -1, 1, -56215112, -552280207989]\) \(-26949791983733109138764089/165161952797784563712000\) \(-120403063589584946946048000\) \([4]\) \(51904512\) \(3.6881\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 139230.eo have rank \(0\).

Complex multiplication

The elliptic curves in class 139230.eo do not have complex multiplication.

Modular form 139230.2.a.eo

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.