Properties

Label 10080bq
Number of curves $2$
Conductor $10080$
CM no
Rank $0$
Graph

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

Elliptic curves in class 10080bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10080.y1 10080bq1 \([0, 0, 0, -1893, 26192]\) \(16079333824/2953125\) \(137781000000\) \([2]\) \(9216\) \(0.85590\) \(\Gamma_0(N)\)-optimal
10080.y2 10080bq2 \([0, 0, 0, 3732, 152192]\) \(1925134784/4465125\) \(-13332791808000\) \([2]\) \(18432\) \(1.2025\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10080bq have rank \(0\).

Complex multiplication

The elliptic curves in class 10080bq do not have complex multiplication.

Modular form 10080.2.a.bq

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 2 q^{11} - 4 q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.