Properties

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

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

Elliptic curves in class 27930dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.dm3 27930dn1 \([1, 0, 0, -1520, -22800]\) \(3301293169/22800\) \(2682397200\) \([2]\) \(24576\) \(0.64272\) \(\Gamma_0(N)\)-optimal
27930.dm2 27930dn2 \([1, 0, 0, -2500, 9932]\) \(14688124849/8122500\) \(955604002500\) \([2, 2]\) \(49152\) \(0.98930\)  
27930.dm4 27930dn3 \([1, 0, 0, 9750, 80982]\) \(871257511151/527800050\) \(-62095148082450\) \([2]\) \(98304\) \(1.3359\)  
27930.dm1 27930dn4 \([1, 0, 0, -30430, 2037650]\) \(26487576322129/44531250\) \(5239057031250\) \([2]\) \(98304\) \(1.3359\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 27930dn do not have complex multiplication.

Modular form 27930.2.a.dn

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