Elliptic curve search results

Results (32 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
259200.a1	259200a1	259200.a	259200a	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{8} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$7.214458730$	$1$		$6$	$587520$	$0.975957$	$61740000$	$1.06884$	$3.21374$	$1$	$[0, 0, 0, -13125, -578750]$	\(y^2=x^3-13125x-578750\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(-66, 2), (-2375/6, 325/6)]$	$1$
259200.b1	259200b1	259200.b	259200b	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$0.560154028$	$1$		$4$	$235008$	$0.517811$	$61740000$	$1.06884$	$2.77270$	$1$	$[0, 0, 0, -2100, 37040]$	\(y^2=x^3-2100x+37040\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(26, 4)]$	$1$
259200.c1	259200c1	259200.c	259200c	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1.603048336$	$1$		$0$	$352512$	$0.720544$	$61740000$	$1.06884$	$2.96786$	$1$	$[0, 0, 0, -4725, -125010]$	\(y^2=x^3-4725x-125010\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(-159/2, 9/2)]$	$1$
259200.d1	259200d1	259200.d	259200d	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1.289471319$	$1$		$2$	$3525120$	$1.871836$	$61740000$	$1.06884$	$4.07618$	$1$	$[0, 0, 0, -472500, 125010000]$	\(y^2=x^3-472500x+125010000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(400, 100)]$	$1$
259200.e1	259200e1	259200.e	259200e	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$705024$	$1.067118$	$61740000$	$1.06884$	$3.30150$	$1$	$[0, 0, 0, -18900, -1000080]$	\(y^2=x^3-18900x-1000080\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$	$1$
259200.f1	259200f1	259200.f	259200f	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$3.267993883$	$1$		$2$	$1762560$	$1.525263$	$61740000$	$1.06884$	$3.74254$	$1$	$[0, 0, 0, -118125, 15626250]$	\(y^2=x^3-118125x+15626250\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(246, 1206)]$	$1$
259200.g1	259200g1	259200.g	259200g	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$4$	$2$	$0$	$1175040$	$1.322531$	$61740000$	$1.06884$	$3.54738$	$1$	$[0, 0, 0, -52500, -4630000]$	\(y^2=x^3-52500x-4630000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$	$1$
259200.h1	259200h1	259200.h	259200h	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$117504$	$0.171238$	$61740000$	$1.06884$	$2.43906$	$1$	$[0, 0, 0, -525, 4630]$	\(y^2=x^3-525x+4630\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$	$1$
259200.gm1	259200gm1	259200.gm	259200gm	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$0.961453665$	$1$		$2$	$705024$	$1.067118$	$61740000$	$1.06884$	$3.30150$	$1$	$[0, 0, 0, -18900, 1000080]$	\(y^2=x^3-18900x+1000080\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(84, 72)]$	$1$
259200.gn1	259200gn1	259200.gn	259200gn	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$35.47801128$	$1$		$0$	$1762560$	$1.525263$	$61740000$	$1.06884$	$3.74254$	$1$	$[0, 0, 0, -118125, -15626250]$	\(y^2=x^3-118125x-15626250\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(-18943581861761039/9755894, 1324000849631189423041/9755894)]$	$1$
259200.go1	259200go1	259200.go	259200go	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$2.499103523$	$1$		$2$	$1175040$	$1.322531$	$61740000$	$1.06884$	$3.54738$	$1$	$[0, 0, 0, -52500, 4630000]$	\(y^2=x^3-52500x+4630000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(126, 124)]$	$1$
259200.gp1	259200gp1	259200.gp	259200gp	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$4$	$2$	$0$	$117504$	$0.171238$	$61740000$	$1.06884$	$2.43906$	$1$	$[0, 0, 0, -525, -4630]$	\(y^2=x^3-525x-4630\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$	$1$
259200.gq1	259200gq1	259200.gq	259200gq	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$587520$	$0.975957$	$61740000$	$1.06884$	$3.21374$	$1$	$[0, 0, 0, -13125, 578750]$	\(y^2=x^3-13125x+578750\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$	$1$
259200.gr1	259200gr1	259200.gr	259200gr	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$4$	$2$	$0$	$235008$	$0.517811$	$61740000$	$1.06884$	$2.77270$	$1$	$[0, 0, 0, -2100, -37040]$	\(y^2=x^3-2100x-37040\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$	$1$
259200.gs1	259200gs1	259200.gs	259200gs	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$7.324068850$	$1$		$0$	$352512$	$0.720544$	$61740000$	$1.06884$	$2.96786$	$1$	$[0, 0, 0, -4725, 125010]$	\(y^2=x^3-4725x+125010\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(1666/3, 63856/3)]$	$1$
259200.gt1	259200gt1	259200.gt	259200gt	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$3525120$	$1.871836$	$61740000$	$1.06884$	$4.07618$	$1$	$[0, 0, 0, -472500, -125010000]$	\(y^2=x^3-472500x-125010000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$	$1$
12700800.g1	-	12700800.g	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$5.503677800$	$1$		$0$	$27495936$	$1.144194$	$61740000$	$1.06884$	$2.57253$	$1$	$[0, 0, 0, -25725, 1588090]$	\(y^2=x^3-25725x+1588090\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(886/3, 2654/3)]$
12700800.h1	-	12700800.h	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{8} \cdot 7^{6} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$51.07235830$	$1$		$2$	$824878080$	$2.844791$	$61740000$	$1.06884$	$3.82012$	$1$	$[0, 0, 0, -23152500, -42878430000]$	\(y^2=x^3-23152500x-42878430000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(-2771, 433), (-1474044/23, 994104/23)]$
12700800.m1	-	12700800.m	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{8} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$274959360$	$2.295486$	$61740000$	$1.06884$	$3.41714$	$1$	$[0, 0, 0, -2572500, -1588090000]$	\(y^2=x^3-2572500x-1588090000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$
12700800.n1	-	12700800.n	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{2} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$82487808$	$1.693499$	$61740000$	$1.06884$	$2.97551$	$1$	$[0, 0, 0, -231525, 42878430]$	\(y^2=x^3-231525x+42878430\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$
12700800.bm1	-	12700800.bm	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$54991872$	$1.490767$	$61740000$	$1.06884$	$2.82678$	$1$	$[0, 0, 0, -102900, -12704720]$	\(y^2=x^3-102900x-12704720\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$
12700800.bn1	-	12700800.bn	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{8} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$1$		$0$	$412439040$	$2.498219$	$61740000$	$1.06884$	$3.56587$	$1$	$[0, 0, 0, -5788125, 5359803750]$	\(y^2=x^3-5788125x+5359803750\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$
12700800.bs1	-	12700800.bs	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{8} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$26.36676907$	$1$		$0$	$137479680$	$1.948912$	$61740000$	$1.06884$	$3.16289$	$1$	$[0, 0, 0, -643125, 198511250]$	\(y^2=x^3-643125x+198511250\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(715457362946/36499, 137701635317118256/36499)]$
12700800.bt1	-	12700800.bt	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{2} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$16$	$2$	$0$	$164975616$	$2.040073$	$61740000$	$1.06884$	$3.22976$	$1$	$[0, 0, 0, -926100, -343027440]$	\(y^2=x^3-926100x-343027440\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$
12700800.vy1	-	12700800.vy	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{8} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$9.569348626$	$1$		$0$	$824878080$	$2.844791$	$61740000$	$1.06884$	$3.82012$	$1$	$[0, 0, 0, -23152500, 42878430000]$	\(y^2=x^3-23152500x+42878430000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(127066/7, 5717636/7)]$
12700800.vz1	-	12700800.vz	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$13.63472111$	$1$		$0$	$27495936$	$1.144194$	$61740000$	$1.06884$	$2.57253$	$1$	$[0, 0, 0, -25725, -1588090]$	\(y^2=x^3-25725x-1588090\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(-6171359/258, 74356631/258)]$
12700800.we1	-	12700800.we	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{2} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$4$	$2$	$0$	$82487808$	$1.693499$	$61740000$	$1.06884$	$2.97551$	$1$	$[0, 0, 0, -231525, -42878430]$	\(y^2=x^3-231525x-42878430\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$
12700800.wf1	-	12700800.wf	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{8} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$7.667872233$	$1$		$0$	$274959360$	$2.295486$	$61740000$	$1.06884$	$3.41714$	$1$	$[0, 0, 0, -2572500, 1588090000]$	\(y^2=x^3-2572500x+1588090000\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(268500/17, 298600/17)]$
12700800.xe1	-	12700800.xe	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{10} \cdot 5^{8} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$1$	$16$	$2$	$0$	$412439040$	$2.498219$	$61740000$	$1.06884$	$3.56587$	$1$	$[0, 0, 0, -5788125, -5359803750]$	\(y^2=x^3-5788125x-5359803750\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[ ]$
12700800.xf1	-	12700800.xf	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{4} \cdot 5^{2} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$11.30587287$	$1$		$0$	$54991872$	$1.490767$	$61740000$	$1.06884$	$2.82678$	$1$	$[0, 0, 0, -102900, 12704720]$	\(y^2=x^3-102900x+12704720\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(1104464/77, 9901732/77)]$
12700800.xk1	-	12700800.xk	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{13} \cdot 3^{10} \cdot 5^{2} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$3.978346320$	$1$		$2$	$164975616$	$2.040073$	$61740000$	$1.06884$	$3.22976$	$1$	$[0, 0, 0, -926100, 343027440]$	\(y^2=x^3-926100x+343027440\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(526, 1196)]$
12700800.xl1	-	12700800.xl	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{7} \cdot 3^{4} \cdot 5^{8} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	8.2.0.2, 5.5.0.1	5S4	$40$	$10$	$0$	$107.6083320$	$1$		$0$	$137479680$	$1.948912$	$61740000$	$1.06884$	$3.16289$	$1$	$[0, 0, 0, -643125, -198511250]$	\(y^2=x^3-643125x-198511250\)	5.5.0.a.1, 8.2.0.b.1, 40.10.0.b.1	$[(-399260865070613295330263777792756180295417872799/29402173479200287370674, 767330924004962095426829636910378353466617903949719222844625389485449/29402173479200287370674)]$

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