Properties

Label 43758.r
Number of curves $2$
Conductor $43758$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43758.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.r1 43758u1 \([1, -1, 1, -27185, 1575969]\) \(3047678972871625/304559880768\) \(222024153079872\) \([2]\) \(172032\) \(1.4892\) \(\Gamma_0(N)\)-optimal
43758.r2 43758u2 \([1, -1, 1, 33655, 7586961]\) \(5783051584712375/37533175779528\) \(-27361685143275912\) \([2]\) \(344064\) \(1.8358\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43758.r have rank \(1\).

Complex multiplication

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

Modular form 43758.2.a.r

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