Properties

Label 4025.e
Number of curves $4$
Conductor $4025$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 4025.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4025.e1 4025a3 \([1, -1, 0, -3092, 66941]\) \(209267191953/55223\) \(862859375\) \([2]\) \(2560\) \(0.69909\)  
4025.e2 4025a2 \([1, -1, 0, -217, 816]\) \(72511713/25921\) \(405015625\) \([2, 2]\) \(1280\) \(0.35251\)  
4025.e3 4025a1 \([1, -1, 0, -92, -309]\) \(5545233/161\) \(2515625\) \([2]\) \(640\) \(0.0059379\) \(\Gamma_0(N)\)-optimal
4025.e4 4025a4 \([1, -1, 0, 658, 5191]\) \(2014698447/1958887\) \(-30607609375\) \([2]\) \(2560\) \(0.69909\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4025.e have rank \(0\).

Complex multiplication

The elliptic curves in class 4025.e do not have complex multiplication.

Modular form 4025.2.a.e

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