Elliptic curve isogeny class with LMFDB label 324870.dd (Cremona label 324870dd)

• Label: 324870.dd
• Number of curves: $8$
• Conductor: $324870$
• CM: no
• Rank: $1$

Elliptic curves in class 324870.dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
324870.dd1	324870dd7	$[1, 1, 1, -110667869061, 14170299110903949]$	$1274090022584975661628188489514561/14072533302105480763470$	$1655619470459407706341482030$	$[2]$	$1207959552$	$4.7923$
324870.dd2	324870dd5	$[1, 1, 1, -6922258911, 221037854331489]$	$311802066473807207098058600161/1033693082103011001480900$	$121612957416337141313226404100$	$[2, 2]$	$603979776$	$4.4457$
324870.dd3	324870dd4	$[1, 1, 1, -6811753131, -216392475356247]$	$297106512928238351998640242081/3977028808593750000$	$467893462302246093750000$	$[2]$	$301989888$	$4.0992$
324870.dd4	324870dd8	$[1, 1, 1, -3939856761, 412769330789829]$	$-57487943130312093140621093761/592356094985924086700006670$	$-69690102218998982876169084718830$	$[2]$	$1207959552$	$4.7923$
324870.dd5	324870dd3	$[1, 1, 1, -624558411, 86810909289]$	$229010110533436633465952161/132501160769452503210000$	$15588629063365317550153290000$	$[2, 2]$	$301989888$	$4.0992$
324870.dd6	324870dd2	$[1, 1, 1, -426108411, -3375030270711]$	$72727020009972527154752161/265361167808100000000$	$31219476031455156900000000$	$[2, 2]$	$150994944$	$3.7526$
324870.dd7	324870dd1	$[1, 1, 1, -14602491, -100595364087]$	$-2926956820564562516641/35459588343029760000$	$-4171785108969108234240000$	$[2]$	$75497472$	$3.4060$	$\Gamma_0(N)$-optimal
324870.dd8	324870dd6	$[1, 1, 1, 2497942089, 697572007089]$	$14651516183052242700771495839/8480668142378708755560900$	$-997742126282712706382984324100$	$[2]$	$603979776$	$4.4457$

Rank

The elliptic curves in class 324870.dd have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$3$	$1 + T$
$5$	$1 + T$
$7$	$1$
$13$	$1 + T$
$17$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 8 T + 23 T^{2}$	1.23.ai
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 324870.dd do not have complex multiplication.

Modular form 324870.2.a.dd

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.