Elliptic curve isogeny class with LMFDB label 406560.cc (Cremona label 406560cc)

• Label: 406560.cc
• Number of curves: $4$
• Conductor: $406560$
• CM: no
• Rank: $1$

Elliptic curves in class 406560.cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
406560.cc1	406560cc2	\([0, -1, 0, -82320, 9113832]\)	\(68017239368/39375\)	\(35714669760000\)	\([2]\)	\(1310720\)	\(1.5461\)	\(\Gamma_0(N)\)-optimal^*
406560.cc2	406560cc4	\([0, -1, 0, -48440, -4028220]\)	\(13858588808/229635\)	\(208287954040320\)	\([2]\)	\(1310720\)	\(1.5461\)
406560.cc3	406560cc1	\([0, -1, 0, -6090, 88200]\)	\(220348864/99225\)	\(11250120974400\)	\([2, 2]\)	\(655360\)	\(1.1996\)	\(\Gamma_0(N)\)-optimal^*
406560.cc4	406560cc3	\([0, -1, 0, 21135, 638145]\)	\(143877824/108045\)	\(-784008430571520\)	\([2]\)	\(1310720\)	\(1.5461\)

^*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 406560.cc1.

Rank

The elliptic curves in class 406560.cc have rank \(1\).

Complex multiplication

The elliptic curves in class 406560.cc do not have complex multiplication.

Modular form 406560.2.a.cc

Isogeny 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

The vertices are labelled with LMFDB labels.