Properties

Label 344850.fs
Number of curves $4$
Conductor $344850$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("344850.fs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 344850.fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
344850.fs1 344850fs4 [1, 1, 1, -9196063, -10737570469] [2] 11796480  
344850.fs2 344850fs3 [1, 1, 1, -665563, -111471469] [2] 11796480  
344850.fs3 344850fs2 [1, 1, 1, -574813, -167917969] [2, 2] 5898240  
344850.fs4 344850fs1 [1, 1, 1, -30313, -3478969] [2] 2949120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 344850.fs have rank \(0\).

Modular form 344850.2.a.fs

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.