Elliptic curve isogeny class with LMFDB label 25410.v (Cremona label 25410w)

• Label: 25410.v
• Number of curves: $8$
• Conductor: $25410$
• CM: no
• Rank: $1$

Elliptic curves in class 25410.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25410.v1	25410w7	\([1, 0, 1, -644204124, 6293317745416]\)	\(16689299266861680229173649/2396798250\)	\(4246074304568250\)	\([2]\)	\(4976640\)	\(3.3214\)
25410.v2	25410w8	\([1, 0, 1, -41321624, 92885463416]\)	\(4404531606962679693649/444872222400201750\)	\(788118279187523812431750\)	\([2]\)	\(4976640\)	\(3.3214\)
25410.v3	25410w6	\([1, 0, 1, -40262874, 98329979416]\)	\(4074571110566294433649/48828650062500\)	\(86502932133372562500\)	\([2, 2]\)	\(2488320\)	\(2.9748\)
25410.v4	25410w5	\([1, 0, 1, -9076334, -10504736728]\)	\(46676570542430835889/106752955783320\)	\(189119373100454162520\)	\([2]\)	\(1658880\)	\(2.7721\)
25410.v5	25410w4	\([1, 0, 1, -7963134, 8609429992]\)	\(31522423139920199089/164434491947880\)	\(291305732989678240680\)	\([2]\)	\(1658880\)	\(2.7721\)
25410.v6	25410w3	\([1, 0, 1, -2450374, 1620729416]\)	\(-918468938249433649/109183593750000\)	\(-193425396527343750000\)	\([2]\)	\(1244160\)	\(2.6282\)
25410.v7	25410w2	\([1, 0, 1, -775734, -32699768]\)	\(29141055407581489/16604321025600\)	\(29415567560432961600\)	\([2, 2]\)	\(829440\)	\(2.4255\)
25410.v8	25410w1	\([1, 0, 1, 192266, -4046968]\)	\(443688652450511/260789760000\)	\(-462004968015360000\)	\([2]\)	\(414720\)	\(2.0789\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 25410.v have rank \(1\).

Complex multiplication

The elliptic curves in class 25410.v do not have complex multiplication.

Modular form 25410.2.a.v

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 4 & 6 & 12 \\ 4 & 1 & 2 & 3 & 12 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 12 & 3 & 6 & 1 & 4 & 12 & 2 & 4 \\ 3 & 12 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.