Properties

Label 482790.dr
Number of curves $6$
Conductor $482790$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dr1")
 
E.isogeny_class()
 

Elliptic curves in class 482790.dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
482790.dr1 482790dr5 \([1, 0, 1, -43017318, 108571018906]\) \(4969327007303723277361/1123462695162150\) \(1990282695704153616150\) \([2]\) \(78643200\) \(3.0791\) \(\Gamma_0(N)\)-optimal*
482790.dr2 482790dr3 \([1, 0, 1, -2996568, 1283392306]\) \(1679731262160129361/570261564022500\) \(1010253146621264122500\) \([2, 2]\) \(39321600\) \(2.7326\) \(\Gamma_0(N)\)-optimal*
482790.dr3 482790dr2 \([1, 0, 1, -1232388, -511837262]\) \(116844823575501841/3760263939600\) \(6661536945101715600\) \([2, 2]\) \(19660800\) \(2.3860\) \(\Gamma_0(N)\)-optimal*
482790.dr4 482790dr1 \([1, 0, 1, -1222708, -520495054]\) \(114113060120923921/124104960\) \(219859507042560\) \([2]\) \(9830400\) \(2.0394\) \(\Gamma_0(N)\)-optimal*
482790.dr5 482790dr4 \([1, 0, 1, 376912, -1752929422]\) \(3342636501165359/751262567039460\) \(-1330907464526992797060\) \([2]\) \(39321600\) \(2.7326\)  
482790.dr6 482790dr6 \([1, 0, 1, 8797302, 8897514778]\) \(42502666283088696719/43898058864843750\) \(-77768089060661458593750\) \([2]\) \(78643200\) \(3.0791\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 482790.dr1.

Rank

sage: E.rank()
 

The elliptic curves in class 482790.dr have rank \(2\).

Complex multiplication

The elliptic curves in class 482790.dr do not have complex multiplication.

Modular form 482790.2.a.dr

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.