Elliptic curve isogeny class with LMFDB label 470925.br (Cremona label 470925br)

• Label: 470925.br
• Number of curves: $3$
• Conductor: $470925$
• CM: no
• Rank: $0$

Elliptic curves in class 470925.br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
470925.br1	470925br3	\([0, 0, 1, -3336673350, 74185445838406]\)	\(-360675992659311050823073792/56219378022244619\)	\(-640373852784630113296875\)	\([]\)	\(226748160\)	\(3.9723\)	\(\Gamma_0(N)\)-optimal^*
470925.br2	470925br2	\([0, 0, 1, -35898600, 128877286531]\)	\(-449167881463536812032/369990050199923699\)	\(-4214417915558505883921875\)	\([]\)	\(75582720\)	\(3.4230\)	\(\Gamma_0(N)\)-optimal^*
470925.br3	470925br1	\([0, 0, 1, 3647400, -2872684094]\)	\(471114356703100928/585612268875179\)	\(-6670489750156335796875\)	\([]\)	\(25194240\)	\(2.8737\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 470925.br1.

Rank

The elliptic curves in class 470925.br have rank \(0\).

Complex multiplication

The elliptic curves in class 470925.br do not have complex multiplication.

Modular form 470925.2.a.br

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.