Properties

Label 46800dm
Number of curves $4$
Conductor $46800$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.s4 46800dm1 \([0, 0, 0, 1725, -58750]\) \(12167/39\) \(-1819584000000\) \([2]\) \(65536\) \(1.0357\) \(\Gamma_0(N)\)-optimal
46800.s3 46800dm2 \([0, 0, 0, -16275, -688750]\) \(10218313/1521\) \(70963776000000\) \([2, 2]\) \(131072\) \(1.3822\)  
46800.s2 46800dm3 \([0, 0, 0, -70275, 6493250]\) \(822656953/85683\) \(3997626048000000\) \([2]\) \(262144\) \(1.7288\)  
46800.s1 46800dm4 \([0, 0, 0, -250275, -48190750]\) \(37159393753/1053\) \(49128768000000\) \([2]\) \(262144\) \(1.7288\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 46800.2.a.dm

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.