Properties

Label 20181d
Number of curves $6$
Conductor $20181$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 20181d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20181.e6 20181d1 \([1, 1, 1, 941, 2840]\) \(103823/63\) \(-55912731903\) \([2]\) \(15360\) \(0.75148\) \(\Gamma_0(N)\)-optimal
20181.e5 20181d2 \([1, 1, 1, -3864, 18216]\) \(7189057/3969\) \(3522502109889\) \([2, 2]\) \(30720\) \(1.0981\)  
20181.e3 20181d3 \([1, 1, 1, -37499, -2793670]\) \(6570725617/45927\) \(40760381557287\) \([2]\) \(61440\) \(1.4446\)  
20181.e2 20181d4 \([1, 1, 1, -47109, 3910266]\) \(13027640977/21609\) \(19178067042729\) \([2, 2]\) \(61440\) \(1.4446\)  
20181.e1 20181d5 \([1, 1, 1, -753444, 251410050]\) \(53297461115137/147\) \(130463041107\) \([2]\) \(122880\) \(1.7912\)  
20181.e4 20181d6 \([1, 1, 1, -32694, 6366582]\) \(-4354703137/17294403\) \(-15348846323197443\) \([2]\) \(122880\) \(1.7912\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20181d have rank \(0\).

Complex multiplication

The elliptic curves in class 20181d do not have complex multiplication.

Modular form 20181.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - 4 q^{11} + q^{12} + 2 q^{13} + q^{14} + 2 q^{15} - q^{16} + 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.