Properties

Label 60984o
Number of curves $2$
Conductor $60984$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.j2 60984o1 \([0, 0, 0, 51909, 8052550]\) \(8788/21\) \(-36964168910355456\) \([2]\) \(337920\) \(1.8630\) \(\Gamma_0(N)\)-optimal
60984.j1 60984o2 \([0, 0, 0, -427251, 89222254]\) \(2450086/441\) \(1552495094234929152\) \([2]\) \(675840\) \(2.2096\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60984o have rank \(0\).

Complex multiplication

The elliptic curves in class 60984o do not have complex multiplication.

Modular form 60984.2.a.o

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