Properties

Label 27930.dm
Number of curves $4$
Conductor $27930$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("27930.dm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27930.dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27930.dm1 27930dn4 [1, 0, 0, -30430, 2037650] [2] 98304  
27930.dm2 27930dn2 [1, 0, 0, -2500, 9932] [2, 2] 49152  
27930.dm3 27930dn1 [1, 0, 0, -1520, -22800] [2] 24576 \(\Gamma_0(N)\)-optimal
27930.dm4 27930dn3 [1, 0, 0, 9750, 80982] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 27930.dm have rank \(0\).

Modular form 27930.2.a.dm

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} + 4q^{11} + q^{12} - 2q^{13} + q^{15} + q^{16} - 2q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.