Properties

Label 76230fa
Number of curves 4
Conductor 76230
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("76230.eu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230fa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.eu3 76230fa1 [1, -1, 1, -545612, -134557761] [2] 1474560 \(\Gamma_0(N)\)-optimal
76230.eu2 76230fa2 [1, -1, 1, -2309792, 1217509791] [2, 2] 2949120  
76230.eu4 76230fa3 [1, -1, 1, 3080758, 6051755031] [2] 5898240  
76230.eu1 76230fa4 [1, -1, 1, -35927222, 82894417719] [2] 5898240  

Rank

sage: E.rank()
 

The elliptic curves in class 76230fa have rank \(0\).

Modular form 76230.2.a.eu

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 2q^{13} + q^{14} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 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.