Properties

Label 360789j
Number of curves $2$
Conductor $360789$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 360789j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360789.j2 360789j1 \([0, 1, 1, -5251531101343, -4637645406687259238]\) \(-32018247290363937163403702272000/44454409555957421205645603\) \(-22238158920666900766172008822951860483\) \([3]\) \(14829143040\) \(6.0704\) \(\Gamma_0(N)\)-optimal
360789.j1 360789j2 \([0, 1, 1, -425515660683913, -3378480795322981367837]\) \(-17032812843524919638015362135588864000/45445783003836939867\) \(-22734089931873408868213806416187\) \([]\) \(44487429120\) \(6.6197\)  

Rank

sage: E.rank()
 

The elliptic curves in class 360789j have rank \(0\).

Complex multiplication

The elliptic curves in class 360789j do not have complex multiplication.

Modular form 360789.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + 5 q^{7} + q^{9} - q^{11} - 2 q^{12} + q^{13} + 4 q^{16} + 5 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.