Properties

Label 43120.h
Number of curves $2$
Conductor $43120$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 43120.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43120.h1 43120bx2 \([0, 1, 0, -43136, 3379060]\) \(18420660721/336875\) \(162336796160000\) \([2]\) \(196608\) \(1.5216\)  
43120.h2 43120bx1 \([0, 1, 0, -16, 153684]\) \(-1/21175\) \(-10204027187200\) \([2]\) \(98304\) \(1.1750\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43120.h have rank \(2\).

Complex multiplication

The elliptic curves in class 43120.h do not have complex multiplication.

Modular form 43120.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.