Properties

Label 46800ek
Number of curves $2$
Conductor $46800$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("ek1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.p1 46800ek1 \([0, 0, 0, -3675, 18250]\) \(117649/65\) \(3032640000000\) \([2]\) \(73728\) \(1.0856\) \(\Gamma_0(N)\)-optimal
46800.p2 46800ek2 \([0, 0, 0, 14325, 144250]\) \(6967871/4225\) \(-197121600000000\) \([2]\) \(147456\) \(1.4321\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46800ek have rank \(0\).

Complex multiplication

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

Modular form 46800.2.a.ek

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