Properties

Label 8280c
Number of curves $2$
Conductor $8280$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 8280c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.b2 8280c1 \([0, 0, 0, 297, -27702]\) \(574992/66125\) \(-333193824000\) \([2]\) \(6912\) \(0.89038\) \(\Gamma_0(N)\)-optimal
8280.b1 8280c2 \([0, 0, 0, -12123, -497178]\) \(9776035692/359375\) \(7243344000000\) \([2]\) \(13824\) \(1.2370\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8280c have rank \(0\).

Complex multiplication

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

Modular form 8280.2.a.c

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