Properties

Label 28611.z
Number of curves 3
Conductor 28611
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("28611.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28611.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28611.z1 28611w3 [0, 0, 1, -20340687, 35309904183] [] 768000  
28611.z2 28611w2 [0, 0, 1, -26877, 3071853] [] 153600  
28611.z3 28611w1 [0, 0, 1, -867, -23337] [] 30720 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28611.z have rank \(1\).

Modular form 28611.2.a.z

sage: E.q_eigenform(10)
 
\( q + 2q^{2} + 2q^{4} + q^{5} + 2q^{7} + 2q^{10} + q^{11} + 4q^{13} + 4q^{14} - 4q^{16} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.