Properties

Label 32490.j
Number of curves $4$
Conductor $32490$
CM no
Rank $1$
Graph

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

Elliptic curves in class 32490.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.j1 32490j4 \([1, -1, 0, -24294465, -44501105219]\) \(46237740924063961/1806561830400\) \(61958652518370484569600\) \([2]\) \(2488320\) \(3.1406\)  
32490.j2 32490j2 \([1, -1, 0, -3582090, 2591768956]\) \(148212258825961/1218375000\) \(41785933917000375000\) \([2]\) \(829440\) \(2.5913\)  
32490.j3 32490j1 \([1, -1, 0, -73170, 94119700]\) \(-1263214441/110808000\) \(-3800320726767192000\) \([2]\) \(414720\) \(2.2447\) \(\Gamma_0(N)\)-optimal
32490.j4 32490j3 \([1, -1, 0, 657855, -2526312515]\) \(918046641959/80912056320\) \(-2774996071386997063680\) \([2]\) \(1244160\) \(2.7941\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32490.j have rank \(1\).

Complex multiplication

The elliptic curves in class 32490.j do not have complex multiplication.

Modular form 32490.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.