Properties

Label 1980d
Number of curves $4$
Conductor $1980$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 1980d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1980.f4 1980d1 \([0, 0, 0, 1968, 123469]\) \(72268906496/606436875\) \(-7073479710000\) \([2]\) \(2304\) \(1.1470\) \(\Gamma_0(N)\)-optimal
1980.f3 1980d2 \([0, 0, 0, -28407, 1696894]\) \(13584145739344/1195803675\) \(223165665043200\) \([2]\) \(4608\) \(1.4936\)  
1980.f2 1980d3 \([0, 0, 0, -140592, 20306401]\) \(-26348629355659264/24169921875\) \(-281917968750000\) \([6]\) \(6912\) \(1.6963\)  
1980.f1 1980d4 \([0, 0, 0, -2249967, 1299009526]\) \(6749703004355978704/5671875\) \(1058508000000\) \([6]\) \(13824\) \(2.0429\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1980d have rank \(0\).

Complex multiplication

The elliptic curves in class 1980d do not have complex multiplication.

Modular form 1980.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2q^{7} - q^{11} + 2q^{13} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.