Elliptic curve isogeny class with Cremona label 25200dz (LMFDB label 25200.p)

• Label: 25200dz
• Number of curves: $8$
• Conductor: $25200$
• CM: no
• Rank: $1$

Elliptic curves in class 25200dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25200.p7	25200dz1	$[0, 0, 0, 755925, 190620250]$	$1023887723039/928972800$	$-43342154956800000000$	$[2]$	$589824$	$2.4553$	$\Gamma_0(N)$-optimal
25200.p6	25200dz2	$[0, 0, 0, -3852075, 1706652250]$	$135487869158881/51438240000$	$2399902525440000000000$	$[2, 2]$	$1179648$	$2.8019$
25200.p5	25200dz3	$[0, 0, 0, -27180075, -53324099750]$	$47595748626367201/1215506250000$	$56710659600000000000000$	$[2, 2]$	$2359296$	$3.1485$
25200.p4	25200dz4	$[0, 0, 0, -54252075, 153763452250]$	$378499465220294881/120530818800$	$5623485881932800000000$	$[2]$	$2359296$	$3.1485$
25200.p8	25200dz5	$[0, 0, 0, 4571925, -170457227750]$	$226523624554079/269165039062500$	$-12558164062500000000000000$	$[2]$	$4718592$	$3.4950$
25200.p2	25200dz6	$[0, 0, 0, -432180075, -3458159099750]$	$191342053882402567201/129708022500$	$6051657497760000000000$	$[2, 2]$	$4718592$	$3.4950$
25200.p3	25200dz7	$[0, 0, 0, -429480075, -3503500199750]$	$-187778242790732059201/4984939585440150$	$-232577341298295638400000000$	$[2]$	$9437184$	$3.8416$
25200.p1	25200dz8	$[0, 0, 0, -6914880075, -221322257999750]$	$783736670177727068275201/360150$	$16803158400000000$	$[2]$	$9437184$	$3.8416$

Rank

The elliptic curves in class 25200dz have rank $1$.

Complex multiplication

The elliptic curves in class 25200dz do not have complex multiplication.

Modular form 25200.2.a.dz

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 Cremona numbering.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.