Properties

Label 10320.p
Number of curves $2$
Conductor $10320$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10320.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10320.p1 10320y2 \([0, -1, 0, -3800, 88560]\) \(1481933914201/53916840\) \(220843376640\) \([2]\) \(13824\) \(0.94645\)  
10320.p2 10320y1 \([0, -1, 0, -600, -3600]\) \(5841725401/1857600\) \(7608729600\) \([2]\) \(6912\) \(0.59988\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10320.p have rank \(0\).

Complex multiplication

The elliptic curves in class 10320.p do not have complex multiplication.

Modular form 10320.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{11} - 2q^{13} - q^{15} - 4q^{17} + 6q^{19} + O(q^{20})\)  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 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.