Properties

Label 43758k
Number of curves $2$
Conductor $43758$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 43758k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.q2 43758k1 \([1, -1, 1, -11450, 333289]\) \(8433606238875/2484248624\) \(48897465666192\) \([2]\) \(116736\) \(1.3325\) \(\Gamma_0(N)\)-optimal
43758.q1 43758k2 \([1, -1, 1, -167510, 26426521]\) \(26409015101734875/3994998436\) \(78633554215788\) \([2]\) \(233472\) \(1.6791\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43758k have rank \(0\).

Complex multiplication

The elliptic curves in class 43758k do not have complex multiplication.

Modular form 43758.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{7} + q^{8} - q^{11} - q^{13} + 2 q^{14} + q^{16} - q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.