Properties

Label 714.f
Number of curves $6$
Conductor $714$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("714.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 714.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
714.f1 714g5 [1, 1, 1, -13718604, -19563199515] [2] 30720  
714.f2 714g3 [1, 1, 1, -859044, -304722459] [2, 2] 15360  
714.f3 714g6 [1, 1, 1, -292604, -699871003] [2] 30720  
714.f4 714g2 [1, 1, 1, -90724, 2605541] [2, 4] 7680  
714.f5 714g1 [1, 1, 1, -70244, 7127525] [8] 3840 \(\Gamma_0(N)\)-optimal
714.f6 714g4 [1, 1, 1, 349916, 20936165] [4] 15360  

Rank

sage: E.rank()
 

The elliptic curves in class 714.f have rank \(0\).

Modular form 714.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - 2q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} - 2q^{13} + q^{14} + 2q^{15} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.