Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32490bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.bu3 32490bv1 \([1, -1, 1, -100787, 12267011]\) \(3301293169/22800\) \(781958997277200\) \([4]\) \(184320\) \(1.6913\) \(\Gamma_0(N)\)-optimal
32490.bu2 32490bv2 \([1, -1, 1, -165767, -5433541]\) \(14688124849/8122500\) \(278572892780002500\) \([2, 2]\) \(368640\) \(2.0379\)  
32490.bu4 32490bv3 \([1, -1, 1, 646483, -43446841]\) \(871257511151/527800050\) \(-18101666572844562450\) \([2]\) \(737280\) \(2.3844\)  
32490.bu1 32490bv4 \([1, -1, 1, -2017697, -1101035329]\) \(26487576322129/44531250\) \(1527263666557031250\) \([2]\) \(737280\) \(2.3844\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32490.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 4q^{11} - 2q^{13} + q^{16} - 2q^{17} + O(q^{20})\)  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 Cremona 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 Cremona labels.