Elliptic curve isogeny class with LMFDB label 476520.cr (Cremona label 476520cr)

• Label: 476520.cr
• Number of curves: $4$
• Conductor: $476520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 476520.cr have rank \(1\).

Complex multiplication

The elliptic curves in class 476520.cr do not have complex multiplication.

Modular form 476520.2.a.cr

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 476520.cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
476520.cr1	476520cr3	\([0, 1, 0, -3812280, 2863734048]\)	\(127191074376964/495\)	\(23846616161280\)	\([2]\)	\(7077888\)	\(2.2030\)	\(\Gamma_0(N)\)-optimal^*
476520.cr2	476520cr2	\([0, 1, 0, -238380, 44641728]\)	\(124386546256/245025\)	\(2951018749958400\)	\([2, 2]\)	\(3538944\)	\(1.8565\)	\(\Gamma_0(N)\)-optimal^*
476520.cr3	476520cr4	\([0, 1, 0, -158960, 74948400]\)	\(-9220796644/45106875\)	\(-2173022897696640000\)	\([2]\)	\(7077888\)	\(2.2030\)
476520.cr4	476520cr1	\([0, 1, 0, -19975, 174470]\)	\(1171019776/658845\)	\(495935095479120\)	\([2]\)	\(1769472\)	\(1.5099\)	\(\Gamma_0(N)\)-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 476520.cr1.