Properties

Label 46800.o
Number of curves $2$
Conductor $46800$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 46800.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.o1 46800fq2 \([0, 0, 0, -1310115, -531840350]\) \(666276475992821/58199166792\) \(21722722606780416000\) \([2]\) \(1179648\) \(2.4510\)  
46800.o2 46800fq1 \([0, 0, 0, -1281315, -558249950]\) \(623295446073461/5458752\) \(2037468266496000\) \([2]\) \(589824\) \(2.1044\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46800.o have rank \(1\).

Complex multiplication

The elliptic curves in class 46800.o do not have complex multiplication.

Modular form 46800.2.a.o

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