↑

Properties

Label 111573.t
Number of curves $2$
Conductor $111573$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 111573.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111573.t1 111573x2 \([1, -1, 1, -147083, 16216134]\) \(11961853903/3078251\) \(90555309172889253\) \([2]\) \(1548288\) \(1.9630\)  
111573.t2 111573x1 \([1, -1, 1, 22702, 1614624]\) \(43986977/64009\) \(-1883002648207527\) \([2]\) \(774144\) \(1.6165\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 111573.t have rank \(1\).

Complex multiplication

The elliptic curves in class 111573.t do not have complex multiplication.

Modular form 111573.2.a.t

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