Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.f2 46800dn1 \([0, 0, 0, -480, 3760]\) \(163840/13\) \(970444800\) \([]\) \(25920\) \(0.46803\) \(\Gamma_0(N)\)-optimal
46800.f1 46800dn2 \([0, 0, 0, -7680, -258320]\) \(671088640/2197\) \(164005171200\) \([]\) \(77760\) \(1.0173\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 46800.2.a.dn

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.