Properties

Label 8280.q
Number of curves $2$
Conductor $8280$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8280.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.q1 8280p2 \([0, 0, 0, -2187, 17766]\) \(28697814/13225\) \(533110118400\) \([2]\) \(7680\) \(0.94490\)  
8280.q2 8280p1 \([0, 0, 0, -1107, -13986]\) \(7443468/115\) \(2317870080\) \([2]\) \(3840\) \(0.59833\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8280.q have rank \(1\).

Complex multiplication

The elliptic curves in class 8280.q do not have complex multiplication.

Modular form 8280.2.a.q

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