Elliptic curves over $\Q$ of conductor 7728

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (43 matches)

 

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
7728.a1	7728j2	7728.a	7728j	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{13} \cdot 3 \cdot 7^{3} \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.247697064$	$1$		$8$	$8640$	$0.794747$	$-2181825073/25039686$	$[0, -1, 0, -432, 15936]$	\(y^2=x^3-x^2-432x+15936\)
7728.a2	7728j1	7728.a	7728j	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{15} \cdot 3^{3} \cdot 7 \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.743091192$	$1$		$4$	$2880$	$0.245441$	$2924207/34776$	$[0, -1, 0, 48, -576]$	\(y^2=x^3-x^2+48x-576\)
7728.b1	7728l4	7728.b	7728l	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{13} \cdot 3^{6} \cdot 7^{4} \cdot 23 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$5.617580568$	$1$		$5$	$92160$	$2.070137$	$632678989847546725777/80515134$	$[0, -1, 0, -2861584, 1864147264]$	\(y^2=x^3-x^2-2861584x+1864147264\)
7728.b2	7728l3	7728.b	7728l	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{13} \cdot 3^{24} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$5.617580568$	$1$		$3$	$92160$	$2.070137$	$231331938231569617/90942310746882$	$[0, -1, 0, -204624, 20243520]$	\(y^2=x^3-x^2-204624x+20243520\)
7728.b3	7728l2	7728.b	7728l	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{14} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2.808790284$	$1$		$9$	$46080$	$1.723562$	$154502321244119857/55101928644$	$[0, -1, 0, -178864, 29166784]$	\(y^2=x^3-x^2-178864x+29166784\)
7728.b4	7728l1	7728.b	7728l	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{16} \cdot 3^{6} \cdot 7 \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1.404395142$	$1$		$7$	$23040$	$1.376987$	$-23771111713777/22848457968$	$[0, -1, 0, -9584, 592320]$	\(y^2=x^3-x^2-9584x+592320\)
7728.c1	7728h4	7728.c	7728h	$4$	$6$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{27} \cdot 3^{2} \cdot 7^{12} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$691200$	$3.053509$	$385693937170561837203625/2159357734550274048$	$[0, -1, 0, -24263848, 45788177008]$	\(y^2=x^3-x^2-24263848x+45788177008\)
7728.c2	7728h2	7728.c	7728h	$4$	$6$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{17} \cdot 3^{6} \cdot 7^{4} \cdot 23^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$230400$	$2.504204$	$155355156733986861625/8291568305839392$	$[0, -1, 0, -1791928, -879068816]$	\(y^2=x^3-x^2-1791928x-879068816\)
7728.c3	7728h3	7728.c	7728h	$4$	$6$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{42} \cdot 3^{4} \cdot 7^{6} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$345600$	$2.706936$	$-8152944444844179625/235342826399858688$	$[0, -1, 0, -670888, 1508909680]$	\(y^2=x^3-x^2-670888x+1508909680\)
7728.c4	7728h1	7728.c	7728h	$4$	$6$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{22} \cdot 3^{12} \cdot 7^{2} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$115200$	$2.157631$	$11079872671250375/324440155855872$	$[0, -1, 0, 74312, -54937232]$	\(y^2=x^3-x^2+74312x-54937232\)
7728.d1	7728i1	7728.d	7728i	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{15} \cdot 7 \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$6.047072195$	$1$		$2$	$47520$	$1.888161$	$-47327266415721472000/1222082060283$	$[0, -1, 0, -478493, -127241151]$	\(y^2=x^3-x^2-478493x-127241151\)
7728.d2	7728i2	7728.d	7728i	$2$	$3$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 23^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.015690731$	$1$		$2$	$142560$	$2.437466$	$-1400832679220224000/150124273180279587$	$[0, -1, 0, -148013, -299020767]$	\(y^2=x^3-x^2-148013x-299020767\)
7728.e1	7728g1	7728.e	7728g	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 3 \cdot 7 \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$800$	$-0.104682$	$512000/483$	$[0, -1, 0, 27, -51]$	\(y^2=x^3-x^2+27x-51\)
7728.f1	7728d1	7728.f	7728d	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{7} \cdot 7 \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$2240$	$0.205352$	$128000/352107$	$[0, -1, 0, 7, -459]$	\(y^2=x^3-x^2+7x-459\)
7728.g1	7728k2	7728.g	7728k	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{15} \cdot 3^{2} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$0.838575060$	$1$		$7$	$9216$	$1.016993$	$5182207647625/91449288$	$[0, -1, 0, -5768, -164112]$	\(y^2=x^3-x^2-5768x-164112\)
7728.g2	7728k1	7728.g	7728k	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{18} \cdot 3^{4} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$1.677150120$	$1$		$5$	$4608$	$0.670420$	$-15625/5842368$	$[0, -1, 0, -8, -7440]$	\(y^2=x^3-x^2-8x-7440\)
7728.h1	7728a2	7728.h	7728a	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.682013834$	$1$		$5$	$5120$	$0.660947$	$26860713266/7394247$	$[0, -1, 0, -792, 6480]$	\(y^2=x^3-x^2-792x+6480\)
7728.h2	7728a1	7728.h	7728a	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{10} \cdot 3^{4} \cdot 7 \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.841006917$	$1$		$7$	$2560$	$0.314373$	$224727548/299943$	$[0, -1, 0, 128, 592]$	\(y^2=x^3-x^2+128x+592\)
7728.i1	7728b4	7728.i	7728b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$1$	$1$		$3$	$16384$	$1.160669$	$369937818893666/123409881$	$[0, -1, 0, -18992, 1013472]$	\(y^2=x^3-x^2-18992x+1013472\)
7728.i2	7728b3	7728.i	7728b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.101	2B	$1$	$1$		$1$	$16384$	$1.160669$	$48260105780546/1193313807$	$[0, -1, 0, -9632, -352800]$	\(y^2=x^3-x^2-9632x-352800\)
7728.i3	7728b2	7728.i	7728b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 3^{4} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.2	2Cs	$1$	$1$		$3$	$8192$	$0.814096$	$267100692772/102880449$	$[0, -1, 0, -1352, 11520]$	\(y^2=x^3-x^2-1352x+11520\)
7728.i4	7728b1	7728.i	7728b	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.60	2B	$1$	$1$		$1$	$4096$	$0.467523$	$8284506032/7394247$	$[0, -1, 0, 268, 1152]$	\(y^2=x^3-x^2+268x+1152\)
7728.j1	7728m1	7728.j	7728m	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{21} \cdot 3 \cdot 7^{11} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.562420442$	$1$		$4$	$95040$	$2.037277$	$83228502970940543/69854999176704$	$[0, -1, 0, 145536, -14389248]$	\(y^2=x^3-x^2+145536x-14389248\)
7728.k1	7728c1	7728.k	7728c	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3 \cdot 7^{3} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$3264$	$0.136544$	$-3525581824/23667$	$[0, -1, 0, -201, 1173]$	\(y^2=x^3-x^2-201x+1173\)
7728.l1	7728n1	7728.l	7728n	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{12} \cdot 3^{5} \cdot 7 \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$12000$	$0.818668$	$-98867482624/20696067$	$[0, -1, 0, -1541, 27693]$	\(y^2=x^3-x^2-1541x+27693\)
7728.m1	7728q2	7728.m	7728q	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{13} \cdot 3^{2} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$0.986172238$	$1$		$7$	$9216$	$0.796187$	$42180533641/22862322$	$[0, 1, 0, -1160, 3444]$	\(y^2=x^3+x^2-1160x+3444\)
7728.m2	7728q1	7728.m	7728q	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{14} \cdot 3^{4} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$0.493086119$	$1$		$11$	$4608$	$0.449614$	$590589719/365148$	$[0, 1, 0, 280, 564]$	\(y^2=x^3+x^2+280x+564\)
7728.n1	7728f1	7728.n	7728f	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{11} \cdot 3^{5} \cdot 7^{3} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.054504924$	$1$		$14$	$4800$	$0.543468$	$-3261064466/1917027$	$[0, 1, 0, -392, 4116]$	\(y^2=x^3+x^2-392x+4116\)
7728.o1	7728r5	7728.o	7728r	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{14} \cdot 3^{16} \cdot 7 \cdot 23^{2} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.32	2B	$1$	$1$		$3$	$98304$	$2.109123$	$54804145548726848737/637608031452$	$[0, 1, 0, -1266144, 547941492]$	\(y^2=x^3+x^2-1266144x+547941492\)
7728.o2	7728r3	7728.o	7728r	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 3^{2} \cdot 7^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.176	2B	$1$	$4$	$2$	$1$	$49152$	$1.762548$	$614716917569296417/19093020912$	$[0, 1, 0, -283424, -58169868]$	\(y^2=x^3+x^2-283424x-58169868\)
7728.o3	7728r4	7728.o	7728r	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 3^{8} \cdot 7^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.25	2Cs	$1$	$1$		$7$	$49152$	$1.762548$	$14447092394873377/1439452851984$	$[0, 1, 0, -81184, 8073716]$	\(y^2=x^3+x^2-81184x+8073716\)
7728.o4	7728r2	7728.o	7728r	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{20} \cdot 3^{4} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.32	2Cs	$1$	$1$		$3$	$24576$	$1.415974$	$169967019783457/26337394944$	$[0, 1, 0, -18464, -832524]$	\(y^2=x^3+x^2-18464x-832524\)
7728.o5	7728r1	7728.o	7728r	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{28} \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.43	2B	$1$	$1$		$1$	$12288$	$1.069401$	$221115865823/664731648$	$[0, 1, 0, 2016, -70668]$	\(y^2=x^3+x^2+2016x-70668\)
7728.o6	7728r6	7728.o	7728r	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{14} \cdot 3^{4} \cdot 7 \cdot 23^{8} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.161	2B	$1$	$1$		$3$	$98304$	$2.109123$	$27207619911317663/177609314617308$	$[0, 1, 0, 100256, 39208820]$	\(y^2=x^3+x^2+100256x+39208820\)
7728.p1	7728u2	7728.p	7728u	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{17} \cdot 3^{8} \cdot 7^{6} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.308634101$	$1$		$11$	$46080$	$1.675484$	$4144806984356137/568114785504$	$[0, 1, 0, -53544, -4183884]$	\(y^2=x^3+x^2-53544x-4183884\)
7728.p2	7728u1	7728.p	7728u	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{22} \cdot 3^{4} \cdot 7^{3} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.617268203$	$1$		$9$	$23040$	$1.328909$	$4101378352343/15049939968$	$[0, 1, 0, 5336, -344908]$	\(y^2=x^3+x^2+5336x-344908\)
7728.q1	7728e2	7728.q	7728e	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 3^{6} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$0.129664739$	$1$		$15$	$21504$	$1.300497$	$1566789944863250/925924041$	$[0, 1, 0, -30728, 2061972]$	\(y^2=x^3+x^2-30728x+2061972\)
7728.q2	7728e1	7728.q	7728e	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{10} \cdot 3^{12} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$0.259329478$	$1$		$13$	$10752$	$0.953924$	$-416618810500/598934007$	$[0, 1, 0, -1568, 44100]$	\(y^2=x^3+x^2-1568x+44100\)
7728.r1	7728t1	7728.r	7728t	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{5} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.207116622$	$1$		$6$	$7200$	$0.673561$	$-7023616000/93934323$	$[0, 1, 0, -253, -7705]$	\(y^2=x^3+x^2-253x-7705\)
7728.s1	7728o1	7728.s	7728o	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{17} \cdot 3^{9} \cdot 7 \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.153035381$	$1$		$8$	$8640$	$1.086926$	$-25727239787761/101406816$	$[0, 1, 0, -9840, 373716]$	\(y^2=x^3+x^2-9840x+373716\)
7728.t1	7728p2	7728.t	7728p	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{23} \cdot 3^{16} \cdot 7^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.644099715$	$1$		$3$	$202752$	$2.442631$	$1733490909744055732873/99355964553216$	$[0, 1, 0, -4004232, -3085271820]$	\(y^2=x^3+x^2-4004232x-3085271820\)
7728.t2	7728p1	7728.t	7728p	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{34} \cdot 3^{8} \cdot 7 \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.288199430$	$1$		$3$	$101376$	$2.096054$	$-354499561600764553/101902222098432$	$[0, 1, 0, -235912, -54035212]$	\(y^2=x^3+x^2-235912x-54035212\)
7728.u1	7728s1	7728.u	7728s	$1$	$1$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( - 2^{25} \cdot 3^{3} \cdot 7^{5} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$37440$	$1.632549$	$-14943832855786297/85501108224$	$[0, 1, 0, -82104, 9072468]$	\(y^2=x^3+x^2-82104x+9072468\)