Properties

Label 145040.k
Number of curves $4$
Conductor $145040$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 145040.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145040.k1 145040g3 \([0, 1, 0, -4135616, -3238495436]\) \(16232905099479601/4052240\) \(1952735165480960\) \([2]\) \(2488320\) \(2.3096\)  
145040.k2 145040g4 \([0, 1, 0, -4119936, -3264254540]\) \(-16048965315233521/256572640900\) \(-123639867921383833600\) \([2]\) \(4976640\) \(2.6562\)  
145040.k3 145040g1 \([0, 1, 0, -58816, -3021516]\) \(46694890801/18944000\) \(9128929918976000\) \([2]\) \(829440\) \(1.7603\) \(\Gamma_0(N)\)-optimal
145040.k4 145040g2 \([0, 1, 0, 192064, -21787340]\) \(1625964918479/1369000000\) \(-659707826176000000\) \([2]\) \(1658880\) \(2.1069\)  

Rank

sage: E.rank()
 

The elliptic curves in class 145040.k have rank \(0\).

Complex multiplication

The elliptic curves in class 145040.k do not have complex multiplication.

Modular form 145040.2.a.k

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{9} - 2 q^{13} + 2 q^{15} - 6 q^{17} + 2 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.