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The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

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Results (1-50 of 220 matches)

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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images MW-generators
46410.a1 46410.a \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $2$ $\Z/2\Z$ $7.899713931$ $[1, 1, 0, -41093, -2836347]$ \(y^2+xy=x^3+x^2-41093x-2836347\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 104.24.0.?, 340.12.0.?, $\ldots$ $[(451, 8178), (231, 138)]$
46410.a2 46410.a \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $1.974928482$ $[1, 1, 0, -10493, 364413]$ \(y^2+xy=x^3+x^2-10493x+364413\) 2.6.0.a.1, 8.12.0-2.a.1.1, 52.12.0-2.a.1.1, 104.24.0.?, 340.12.0.?, $\ldots$ $[(29, 278), (-7, 665)]$
46410.a3 46410.a \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $2$ $\Z/2\Z$ $1.974928482$ $[1, 1, 0, -10173, 390717]$ \(y^2+xy=x^3+x^2-10173x+390717\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 52.12.0-4.c.1.2, 104.24.0.?, $\ldots$ $[(-6, 675), (59, -14)]$
46410.a4 46410.a \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $2$ $\Z/2\Z$ $1.974928482$ $[1, 1, 0, 14987, 1888117]$ \(y^2+xy=x^3+x^2+14987x+1888117\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 52.12.0-4.c.1.1, 104.24.0.?, $\ldots$ $[(21, 1477), (97, 2017)]$
46410.b1 46410.b \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -516418, 138505948]$ \(y^2+xy=x^3+x^2-516418x+138505948\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0-4.c.1.2, 120.24.0.?, $\ldots$ $[ ]$
46410.b2 46410.b \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 0, -79018, -5573612]$ \(y^2+xy=x^3+x^2-79018x-5573612\) 2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 6188.12.0.?, $\ldots$ $[ ]$
46410.b3 46410.b \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -71018, -7312812]$ \(y^2+xy=x^3+x^2-71018x-7312812\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.4, 120.24.0.?, $\ldots$ $[ ]$
46410.b4 46410.b \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, 230382, -38184372]$ \(y^2+xy=x^3+x^2+230382x-38184372\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0-4.c.1.1, 120.24.0.?, $\ldots$ $[ ]$
46410.c1 46410.c \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $1.028728940$ $[1, 1, 0, -240473, 45288633]$ \(y^2+xy=x^3+x^2-240473x+45288633\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 52.12.0-4.c.1.2, 156.24.0.?, $\ldots$ $[(283, -133)]$
46410.c2 46410.c \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.514364470$ $[1, 1, 0, -15053, 700557]$ \(y^2+xy=x^3+x^2-15053x+700557\) 2.6.0.a.1, 12.12.0-2.a.1.1, 52.12.0-2.a.1.1, 140.12.0.?, 156.24.0.?, $\ldots$ $[(79, 71)]$
46410.c3 46410.c \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $1.028728940$ $[1, 1, 0, -5953, 1550497]$ \(y^2+xy=x^3+x^2-5953x+1550497\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 52.12.0-4.c.1.1, 140.12.0.?, $\ldots$ $[(-61, 1331)]$
46410.c4 46410.c \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $1.028728940$ $[1, 1, 0, -1533, -5187]$ \(y^2+xy=x^3+x^2-1533x-5187\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 104.12.0.?, 140.12.0.?, $\ldots$ $[(-22, 147)]$
46410.d1 46410.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $134.1067798$ $[1, 1, 0, -389305321043, -93494136872571087]$ \(y^2+xy=x^3+x^2-389305321043x-93494136872571087\) 2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 40.12.0-4.c.1.5, 52.12.0-4.c.1.1, $\ldots$ $[(1508601471872507885983985627371936709757566823225800653018719/1366673739905009915296034899, 879459458869071935918731825228173637973833771473035324607973288740209267480667812717964372/1366673739905009915296034899)]$
46410.d2 46410.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $67.05338990$ $[1, 1, 0, -24333584823, -1460601042571323]$ \(y^2+xy=x^3+x^2-24333584823x-1460601042571323\) 2.6.0.a.1, 20.12.0-2.a.1.1, 28.12.0-2.a.1.1, 52.12.0-2.a.1.1, 140.24.0.?, $\ldots$ $[(-4081259501510322207771879748947/6744879943573, 207690865303260286180352679243344876030058792/6744879943573)]$
46410.d3 46410.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $134.1067798$ $[1, 1, 0, -20930167323, -1883681914046823]$ \(y^2+xy=x^3+x^2-20930167323x-1883681914046823\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 28.12.0-4.c.1.1, 70.6.0.a.1, $\ldots$ $[(15290300560336145784416667491093032534255737588366974525873/153071294353598674559152217, 1835905916689334865577826566575814517941349914356412103523088227129921753252822229004288/153071294353598674559152217)]$
46410.d4 46410.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $33.52669495$ $[1, 1, 0, -1735564903, -15959344729547]$ \(y^2+xy=x^3+x^2-1735564903x-15959344729547\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 52.12.0-4.c.1.2, 56.12.0-4.c.1.5, $\ldots$ $[(-2933810903143538/313297, 93805596483445740048481/313297)]$
46410.e1 46410.e \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\mathsf{trivial}$ $3.236349211$ $[1, 1, 0, -92228, -47906022]$ \(y^2+xy=x^3+x^2-92228x-47906022\) 37128.2.0.? $[(979, 27818)]$
46410.f1 46410.f \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, -11522913, -15163667757]$ \(y^2+xy=x^3+x^2-11522913x-15163667757\) 26520.2.0.? $[ ]$
46410.g1 46410.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -2507978363, 48341976384717]$ \(y^2+xy=x^3+x^2-2507978363x+48341976384717\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.1, 42.6.0.a.1, $\ldots$ $[ ]$
46410.g2 46410.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -215146843, 142578285613]$ \(y^2+xy=x^3+x^2-215146843x+142578285613\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.2, 168.24.0.?, $\ldots$ $[ ]$
46410.g3 46410.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 0, -156836843, 754401791613]$ \(y^2+xy=x^3+x^2-156836843x+754401791613\) 2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 84.24.0.?, 340.12.0.?, $\ldots$ $[ ]$
46410.g4 46410.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -6246123, 20452740477]$ \(y^2+xy=x^3+x^2-6246123x+20452740477\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.5, 168.24.0.?, $\ldots$ $[ ]$
46410.h1 46410.h \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $5.953223749$ $[1, 1, 0, -10154908218, 176807644788372]$ \(y^2+xy=x^3+x^2-10154908218x+176807644788372\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 84.12.0.?, 104.24.0.?, $\ldots$ $[(12899, 6919291)]$
46410.h2 46410.h \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $2.976611874$ $[1, 1, 0, -8508508218, 301913300148372]$ \(y^2+xy=x^3+x^2-8508508218x+301913300148372\) 2.6.0.a.1, 8.12.0-2.a.1.1, 52.12.0-2.a.1.1, 84.12.0.?, 104.24.0.?, $\ldots$ $[(43524, 3725310)]$
46410.h3 46410.h \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $5.953223749$ $[1, 1, 0, -8507197498, 302011019305108]$ \(y^2+xy=x^3+x^2-8507197498x+302011019305108\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 52.12.0-4.c.1.2, 84.12.0.?, $\ldots$ $[(54933, 648275)]$
46410.h4 46410.h \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $5.953223749$ $[1, 1, 0, -6883079738, 420764955691668]$ \(y^2+xy=x^3+x^2-6883079738x+420764955691668\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 52.12.0-4.c.1.1, 104.24.0.?, $\ldots$ $[(80873, 19785380)]$
46410.i1 46410.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -381913, -91003007]$ \(y^2+xy=x^3+x^2-381913x-91003007\) 2.3.0.a.1, 4.6.0.c.1, 52.12.0-4.c.1.1, 68.12.0-4.c.1.1, 280.12.0.?, $\ldots$ $[ ]$
46410.i2 46410.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -35793, 127737]$ \(y^2+xy=x^3+x^2-35793x+127737\) 2.3.0.a.1, 4.6.0.c.1, 68.12.0-4.c.1.2, 104.12.0.?, 140.12.0.?, $\ldots$ $[ ]$
46410.i3 46410.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 0, -23893, -1426403]$ \(y^2+xy=x^3+x^2-23893x-1426403\) 2.6.0.a.1, 52.12.0-2.a.1.1, 68.12.0-2.a.1.1, 140.12.0.?, 884.24.0.?, $\ldots$ $[ ]$
46410.i4 46410.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -773, -43827]$ \(y^2+xy=x^3+x^2-773x-43827\) 2.3.0.a.1, 4.6.0.c.1, 52.12.0-4.c.1.2, 136.12.0.?, 140.12.0.?, $\ldots$ $[ ]$
46410.j1 46410.j \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $8.171952159$ $[1, 1, 0, -3427203, -2443497147]$ \(y^2+xy=x^3+x^2-3427203x-2443497147\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 104.24.0.?, 1428.12.0.?, $\ldots$ $[(2471, 63441)]$
46410.j2 46410.j \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $4.085976079$ $[1, 1, 0, -214203, -38245347]$ \(y^2+xy=x^3+x^2-214203x-38245347\) 2.6.0.a.1, 8.12.0-2.a.1.1, 52.12.0-2.a.1.1, 104.24.0.?, 1428.12.0.?, $\ldots$ $[(959, 24808)]$
46410.j3 46410.j \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $2.042988039$ $[1, 1, 0, -201203, -43073547]$ \(y^2+xy=x^3+x^2-201203x-43073547\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 52.12.0-4.c.1.1, 104.24.0.?, $\ldots$ $[(739, 14208)]$
46410.j4 46410.j \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $8.171952159$ $[1, 1, 0, -14203, -525347]$ \(y^2+xy=x^3+x^2-14203x-525347\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 52.12.0-4.c.1.2, 104.24.0.?, $\ldots$ $[(25062/7, 3767611/7)]$
46410.k1 46410.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $1.667772382$ $[1, 1, 0, -6008, -119538]$ \(y^2+xy=x^3+x^2-6008x-119538\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 104.24.0.?, 1428.12.0.?, $\ldots$ $[(-23, 96)]$
46410.k2 46410.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.833886191$ $[1, 1, 0, -2438, 43968]$ \(y^2+xy=x^3+x^2-2438x+43968\) 2.6.0.a.1, 8.12.0-2.a.1.1, 52.12.0-2.a.1.1, 104.24.0.?, 1428.12.0.?, $\ldots$ $[(-2, 222)]$
46410.k3 46410.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $1.667772382$ $[1, 1, 0, -2418, 44772]$ \(y^2+xy=x^3+x^2-2418x+44772\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 52.12.0-4.c.1.2, 104.24.0.?, $\ldots$ $[(29, -5)]$
46410.k4 46410.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $0.416943095$ $[1, 1, 0, 812, 156418]$ \(y^2+xy=x^3+x^2+812x+156418\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 52.12.0-4.c.1.1, 104.24.0.?, $\ldots$ $[(-11, 388)]$
46410.l1 46410.l \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\mathsf{trivial}$ $10.02496614$ $[1, 1, 0, -29668, -1979312]$ \(y^2+xy=x^3+x^2-29668x-1979312\) 37128.2.0.? $[(33621/13, 229321/13)]$
46410.m1 46410.m \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $1.417006956$ $[1, 1, 0, -156207, 23697189]$ \(y^2+xy=x^3+x^2-156207x+23697189\) 2.3.0.a.1, 204.6.0.?, 1820.6.0.?, 92820.12.0.? $[(230, -63)]$
46410.m2 46410.m \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $2.834013912$ $[1, 1, 0, -9327, 402021]$ \(y^2+xy=x^3+x^2-9327x+402021\) 2.3.0.a.1, 204.6.0.?, 910.6.0.?, 92820.12.0.? $[(-50, 889)]$
46410.n1 46410.n \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $0.978535019$ $[1, 1, 0, -951307, 356736229]$ \(y^2+xy=x^3+x^2-951307x+356736229\) 2.3.0.a.1, 4.6.0.c.1, 104.12.0.?, 140.12.0.?, 408.12.0.?, $\ldots$ $[(565, -188)]$
46410.n2 46410.n \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.489267509$ $[1, 1, 0, -59507, 5545389]$ \(y^2+xy=x^3+x^2-59507x+5545389\) 2.6.0.a.1, 104.12.0.?, 140.12.0.?, 204.12.0.?, 3640.24.0.?, $\ldots$ $[(173, 596)]$
46410.n3 46410.n \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $0.978535019$ $[1, 1, 0, -32987, 10547061]$ \(y^2+xy=x^3+x^2-32987x+10547061\) 2.3.0.a.1, 4.6.0.c.1, 104.12.0.?, 204.12.0.?, 280.12.0.?, $\ldots$ $[(37, 3044)]$
46410.n4 46410.n \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $0.978535019$ $[1, 1, 0, -5427, -3219]$ \(y^2+xy=x^3+x^2-5427x-3219\) 2.3.0.a.1, 4.6.0.c.1, 104.12.0.?, 140.12.0.?, 204.12.0.?, $\ldots$ $[(95, 544)]$
46410.o1 46410.o \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $0.541854454$ $[1, 1, 0, -3887, -89739]$ \(y^2+xy=x^3+x^2-3887x-89739\) 2.3.0.a.1, 204.6.0.?, 1820.6.0.?, 92820.12.0.? $[(-38, 89)]$
46410.o2 46410.o \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $1.083708909$ $[1, 1, 0, 193, -5691]$ \(y^2+xy=x^3+x^2+193x-5691\) 2.3.0.a.1, 204.6.0.?, 910.6.0.?, 92820.12.0.? $[(30, 153)]$
46410.p1 46410.p \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $5.974411570$ $[1, 1, 0, -740012, -245331216]$ \(y^2+xy=x^3+x^2-740012x-245331216\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.2, 120.24.0.?, $\ldots$ $[(4615, 305357)]$
46410.p2 46410.p \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z$ $5.974411570$ $[1, 1, 0, -90092, 4453296]$ \(y^2+xy=x^3+x^2-90092x+4453296\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0-4.c.1.5, 120.24.0.?, $\ldots$ $[(301, 2022)]$
46410.p3 46410.p \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $2.987205785$ $[1, 1, 0, -46412, -3819696]$ \(y^2+xy=x^3+x^2-46412x-3819696\) 2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 364.12.0.?, $\ldots$ $[(-115, 173)]$
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