↑

Properties

Label 146523.z
Number of curves $2$
Conductor $146523$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 146523.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.z1 146523t1 \([1, 0, 1, -1124361, 321236047]\) \(274625/81\) \(46364483394895253913\) \([2]\) \(3760128\) \(2.4793\) \(\Gamma_0(N)\)-optimal
146523.z2 146523t2 \([1, 0, 1, 3027124, 2141247071]\) \(5359375/6561\) \(-3755523154986515566953\) \([2]\) \(7520256\) \(2.8259\)  

Rank

sage: E.rank()
 

The elliptic curves in class 146523.z have rank \(0\).

Complex multiplication

The elliptic curves in class 146523.z do not have complex multiplication.

Modular form 146523.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} - 4 q^{7} - 3 q^{8} + q^{9} + 4 q^{11} - q^{12} - 4 q^{14} - q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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.