↑

Properties

Label 182070.dp
Number of curves $2$
Conductor $182070$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dp1")
 
E.isogeny_class()
 

Elliptic curves in class 182070.dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.dp1 182070bu1 \([1, -1, 1, -13328012, -18684404081]\) \(551105805571803/1376829440\) \(654131351136500858880\) \([2]\) \(16558080\) \(2.8715\) \(\Gamma_0(N)\)-optimal
182070.dp2 182070bu2 \([1, -1, 1, -8334092, -32859146609]\) \(-134745327251163/903920796800\) \(-429452563224655075593600\) \([2]\) \(33116160\) \(3.2181\)  

Rank

sage: E.rank()
 

The elliptic curves in class 182070.dp have rank \(0\).

Complex multiplication

The elliptic curves in class 182070.dp do not have complex multiplication.

Modular form 182070.2.a.dp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 4 q^{11} + 6 q^{13} + q^{14} + q^{16} + 6 q^{19} + O(q^{20})\) 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.