↑

Properties

Label 485520.dh
Number of curves $4$
Conductor $485520$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("dh1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 485520.dh have rank \(1\).

Complex multiplication

The elliptic curves in class 485520.dh do not have complex multiplication.

Modular form 485520.2.a.dh

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - 4 q^{11} + 2 q^{13} - q^{15} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 485520.dh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
485520.dh1 485520dh4 \([0, -1, 0, -131880, -18369600]\) \(10262905636/13125\) \(324408927360000\) \([2]\) \(2621440\) \(1.6923\)  
485520.dh2 485520dh3 \([0, -1, 0, -97200, 11607792]\) \(4108974916/36015\) \(890178096675840\) \([2]\) \(2621440\) \(1.6923\) \(\Gamma_0(N)\)-optimal*
485520.dh3 485520dh2 \([0, -1, 0, -10500, -114048]\) \(20720464/11025\) \(68125874745600\) \([2, 2]\) \(1310720\) \(1.3457\) \(\Gamma_0(N)\)-optimal*
485520.dh4 485520dh1 \([0, -1, 0, 2505, -15210]\) \(4499456/2835\) \(-1094880129840\) \([2]\) \(655360\) \(0.99917\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 485520.dh1.