Elliptic curve isogeny class with LMFDB label 110670.cm (Cremona label 110670cp)

• Label: 110670.cm
• Number of curves: $8$
• Conductor: $110670$
• CM: no
• Rank: $0$

Elliptic curves in class 110670.cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110670.cm1	110670cp8	$[1, 0, 0, -258731208280, -50654853221670100]$	$1915447099311696788795300773853656437121/2359330710565906457438184052500$	$2359330710565906457438184052500$	$[2]$	$788529152$	$5.1081$
110670.cm2	110670cp4	$[1, 0, 0, -36426360100, 2675908664482832]$	$5345287166085790635663218704920974401/226978257155929261920000$	$226978257155929261920000$	$[8]$	$197132288$	$4.4149$
110670.cm3	110670cp6	$[1, 0, 0, -16306945780, -777467273017600]$	$479558500651862026155270257138637121/16398477508430925116750756250000$	$16398477508430925116750756250000$	$[2, 2]$	$394264576$	$4.7615$
110670.cm4	110670cp3	$[1, 0, 0, -2525695780, 32101233232400]$	$1781832302709884421209712638637121/585975791707934414062500000000$	$585975791707934414062500000000$	$[2, 4]$	$197132288$	$4.4149$
110670.cm5	110670cp2	$[1, 0, 0, -2276760100, 41806588162832]$	$1305195379419707692723460338574401/268915325631261926400000000$	$268915325631261926400000000$	$[2, 8]$	$98566144$	$4.0683$
110670.cm6	110670cp1	$[1, 0, 0, -126851620, 800523760400]$	$-225741686871429146260559062081/146211902909299839467520000$	$-146211902909299839467520000$	$[8]$	$49283072$	$3.7218$	$\Gamma_0(N)$-optimal
110670.cm7	110670cp7	$[1, 0, 0, 5617316720, -2712410599365100]$	$19602454118850102896203267379162879/3189643093950949672061474484052500$	$-3189643093950949672061474484052500$	$[2]$	$788529152$	$5.1081$
110670.cm8	110670cp5	$[1, 0, 0, 7272583340, 220528019677472]$	$42539250356844378683161410804461759/45626792684197425842285156250000$	$-45626792684197425842285156250000$	$[4]$	$394264576$	$4.7615$

Rank

The elliptic curves in class 110670.cm have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$3$	$1 - T$
$5$	$1 - T$
$7$	$1 - T$
$17$	$1 - T$
$31$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 - 8 T + 23 T^{2}$	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 110670.cm do not have complex multiplication.

Modular form 110670.2.a.cm

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.