↑

Properties

Label 28594.e
Number of curves $4$
Conductor $28594$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 28594.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28594.e1 28594f4 \([1, 1, 0, -95050, -7833894]\) \(159661140625/48275138\) \(28715177906893298\) \([2]\) \(302400\) \(1.8631\)  
28594.e2 28594f3 \([1, 1, 0, -86640, -9850612]\) \(120920208625/19652\) \(11689467904292\) \([2]\) \(151200\) \(1.5166\)  
28594.e3 28594f2 \([1, 1, 0, -36180, 2633192]\) \(8805624625/2312\) \(1375231518152\) \([2]\) \(100800\) \(1.3138\)  
28594.e4 28594f1 \([1, 1, 0, -2540, 29456]\) \(3048625/1088\) \(647167773248\) \([2]\) \(50400\) \(0.96726\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28594.e have rank \(0\).

Complex multiplication

The elliptic curves in class 28594.e do not have complex multiplication.

Modular form 28594.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - q^{8} + q^{9} - 6 q^{11} + 2 q^{12} + 2 q^{13} + 4 q^{14} + q^{16} + q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.