Properties

Label 283220o
Number of curves $2$
Conductor $283220$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 283220o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283220.o1 283220o1 \([0, -1, 0, -287940, 59602600]\) \(-177953104/125\) \(-1854537701408000\) \([]\) \(1990656\) \(1.8660\) \(\Gamma_0(N)\)-optimal
283220.o2 283220o2 \([0, -1, 0, 278500, 252645352]\) \(161017136/1953125\) \(-28977151584500000000\) \([]\) \(5971968\) \(2.4153\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283220o have rank \(1\).

Complex multiplication

The elliptic curves in class 283220o do not have complex multiplication.

Modular form 283220.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2 q^{9} - 6 q^{11} + 2 q^{13} - q^{15} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.