Properties

Label 23064m
Number of curves $6$
Conductor $23064$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23064m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23064.i5 23064m1 \([0, 1, 0, 641, -7510]\) \(2048/3\) \(-42600176688\) \([2]\) \(14400\) \(0.72507\) \(\Gamma_0(N)\)-optimal
23064.i4 23064m2 \([0, 1, 0, -4164, -78624]\) \(35152/9\) \(2044808481024\) \([2, 2]\) \(28800\) \(1.0716\)  
23064.i3 23064m3 \([0, 1, 0, -23384, 1305216]\) \(1556068/81\) \(73613105316864\) \([2, 2]\) \(57600\) \(1.4182\)  
23064.i2 23064m4 \([0, 1, 0, -61824, -5936880]\) \(28756228/3\) \(2726411308032\) \([2]\) \(57600\) \(1.4182\)  
23064.i6 23064m5 \([0, 1, 0, 15056, 5210720]\) \(207646/6561\) \(-11925323061331968\) \([2]\) \(115200\) \(1.7648\)  
23064.i1 23064m6 \([0, 1, 0, -369344, 86272992]\) \(3065617154/9\) \(16358467848192\) \([2]\) \(115200\) \(1.7648\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23064m have rank \(0\).

Complex multiplication

The elliptic curves in class 23064m do not have complex multiplication.

Modular form 23064.2.a.m

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.