Properties

Label 485520.h
Number of curves $2$
Conductor $485520$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 485520.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
485520.h1 485520h2 \([0, -1, 0, -37454388536, -2789974521369360]\) \(58773069105954437388714841/21507018750\) \(2126344802559667200000\) \([2]\) \(530841600\) \(4.3501\) \(\Gamma_0(N)\)-optimal*
485520.h2 485520h1 \([0, -1, 0, -2340888536, -43593186969360]\) \(-14348696196102335214841/274485585937500\) \(-27137698898214240000000000\) \([2]\) \(265420800\) \(4.0035\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 485520.h1.

Rank

sage: E.rank()
 

The elliptic curves in class 485520.h have rank \(0\).

Complex multiplication

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

Modular form 485520.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - 2 q^{11} + 2 q^{13} + q^{15} + 4 q^{19} + O(q^{20})\) 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 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.