Properties

Label 152592bq
Number of curves $2$
Conductor $152592$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bq1")
 
E.isogeny_class()
 

Elliptic curves in class 152592bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152592.i2 152592bq1 \([0, -1, 0, -1223144, 26145648]\) \(2046931732873/1181672448\) \(116828980219899543552\) \([2]\) \(3317760\) \(2.5401\) \(\Gamma_0(N)\)-optimal
152592.i1 152592bq2 \([0, -1, 0, -13800424, 19686949744]\) \(2940001530995593/8673562656\) \(857533305180255289344\) \([2]\) \(6635520\) \(2.8867\)  

Rank

sage: E.rank()
 

The elliptic curves in class 152592bq have rank \(0\).

Complex multiplication

The elliptic curves in class 152592bq do not have complex multiplication.

Modular form 152592.2.a.bq

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - 2 q^{7} + q^{9} - q^{11} + 2 q^{15} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.