Elliptic curve search results

Results (26 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
3192.h1	3192j3	3192.h	3192j	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3 \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.102	2B	$456$	$48$	$0$	$1$	$4$	$2$	$1$	$5120$	$0.988599$	$1823652903746/328593657$	$0.93527$	$4.44406$	$[0, -1, 0, -3232, -57620]$	\(y^2=x^3-x^2-3232x-57620\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 228.12.0.?, 456.48.0.?	$[]$
6384.bg1	6384p3	6384.bg	6384p	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3 \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.104	2B	$456$	$48$	$0$	$1$	$1$		$1$	$10240$	$0.988599$	$1823652903746/328593657$	$0.93527$	$4.09248$	$[0, 1, 0, -3232, 57620]$	\(y^2=x^3+x^2-3232x+57620\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.7, 228.12.0.?, 456.48.0.?	$[]$
9576.e1	9576g3	9576.e	9576g	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3^{7} \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$1$	$1$		$1$	$40960$	$1.537905$	$1823652903746/328593657$	$0.93527$	$4.63053$	$[0, 0, 0, -29091, 1584830]$	\(y^2=x^3-29091x+1584830\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.7, 76.12.0.?, $\ldots$	$[]$
19152.h1	19152ba3	19152.h	19152ba	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3^{7} \cdot 7^{8} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$1.121371363$	$1$		$23$	$81920$	$1.537905$	$1823652903746/328593657$	$0.93527$	$4.30502$	$[0, 0, 0, -29091, -1584830]$	\(y^2=x^3-29091x-1584830\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.5, 76.12.0.?, $\ldots$	$[(-67, 252), (-81, 490)]$
22344.r1	22344bj4	22344.r	22344bj	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{11} \cdot 3 \cdot 7^{14} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$3192$	$48$	$0$	$16.45809837$	$1$		$1$	$245760$	$1.961554$	$1823652903746/328593657$	$0.93527$	$4.74640$	$[0, 1, 0, -158384, 20080416]$	\(y^2=x^3+x^2-158384x+20080416\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 56.24.0-8.m.1.1, 456.24.0.?, $\ldots$	$[(12410457/184, 21044562435/184)]$
25536.m1	25536ch4	25536.m	25536ch	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{17} \cdot 3 \cdot 7^{8} \cdot 19 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.53	2B	$456$	$48$	$0$	$3.185632658$	$1$		$7$	$81920$	$1.335173$	$1823652903746/328593657$	$0.93527$	$3.94324$	$[0, -1, 0, -12929, 473889]$	\(y^2=x^3-x^2-12929x+473889\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 456.48.0.?	$[(-75, 1008)]$
25536.ce1	25536bj4	25536.ce	25536bj	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{17} \cdot 3 \cdot 7^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.63	2B	$456$	$48$	$0$	$6.903003359$	$1$		$1$	$81920$	$1.335173$	$1823652903746/328593657$	$0.93527$	$3.94324$	$[0, 1, 0, -12929, -473889]$	\(y^2=x^3+x^2-12929x-473889\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.3, 456.48.0.?	$[(741/2, 15015/2)]$
44688.j1	44688g4	44688.j	44688g	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{11} \cdot 3 \cdot 7^{14} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$491520$	$1.961554$	$1823652903746/328593657$	$0.93527$	$4.43914$	$[0, -1, 0, -158384, -20080416]$	\(y^2=x^3-x^2-158384x-20080416\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 56.24.0-8.m.1.2, 456.24.0.?, $\ldots$	$[]$
60648.bm1	60648o4	60648.bm	60648o	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{11} \cdot 3 \cdot 7^{8} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$43.96662372$	$1$		$1$	$1843200$	$2.460819$	$1823652903746/328593657$	$0.93527$	$4.86006$	$[0, 1, 0, -1166872, 402216560]$	\(y^2=x^3+x^2-1166872x+402216560\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.3, $\ldots$	$[(209793968745042174457/422681572, 1929098235602344229984189779605/422681572)]$
67032.ci1	67032bf4	67032.ci	67032bf	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{11} \cdot 3^{7} \cdot 7^{14} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$3192$	$48$	$0$	$1$	$16$	$2$	$1$	$1966080$	$2.510860$	$1823652903746/328593657$	$0.93527$	$4.87033$	$[0, 0, 0, -1425459, -543596690]$	\(y^2=x^3-1425459x-543596690\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 168.24.0.?, 456.24.0.?, $\ldots$	$[]$
76608.ed1	76608bv4	76608.ed	76608bv	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{17} \cdot 3^{7} \cdot 7^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$10.65614714$	$1$		$1$	$655360$	$1.884478$	$1823652903746/328593657$	$0.93527$	$4.14415$	$[0, 0, 0, -116364, 12678640]$	\(y^2=x^3-116364x+12678640\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.1, 24.24.0-8.m.1.6, $\ldots$	$[(115985/14, 33723495/14)]$
76608.fd1	76608ey4	76608.fd	76608ey	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{17} \cdot 3^{7} \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$1$	$1$		$1$	$655360$	$1.884478$	$1823652903746/328593657$	$0.93527$	$4.14415$	$[0, 0, 0, -116364, -12678640]$	\(y^2=x^3-116364x-12678640\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.8, $\ldots$	$[]$
79800.bn1	79800k4	79800.bn	79800k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3 \cdot 5^{6} \cdot 7^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$2280$	$48$	$0$	$3.854116680$	$1$		$1$	$655360$	$1.793318$	$1823652903746/328593657$	$0.93527$	$4.03225$	$[0, 1, 0, -80808, -7364112]$	\(y^2=x^3+x^2-80808x-7364112\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 40.24.0-8.m.1.2, 456.24.0.?, $\ldots$	$[(-427/2, 1911/2)]$
121296.bq1	121296r4	121296.bq	121296r	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{11} \cdot 3 \cdot 7^{8} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$1.882390073$	$1$		$5$	$3686400$	$2.460819$	$1823652903746/328593657$	$0.93527$	$4.57228$	$[0, -1, 0, -1166872, -402216560]$	\(y^2=x^3-x^2-1166872x-402216560\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.1, $\ldots$	$[(-480, 6860)]$
134064.er1	134064ex3	134064.er	134064ex	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{11} \cdot 3^{7} \cdot 7^{14} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$3192$	$48$	$0$	$2.746831158$	$1$		$5$	$3932160$	$2.510860$	$1823652903746/328593657$	$0.93527$	$4.58439$	$[0, 0, 0, -1425459, 543596690]$	\(y^2=x^3-1425459x+543596690\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 168.24.0.?, 456.24.0.?, $\ldots$	$[(973, 8820)]$
159600.bq1	159600gz3	159600.bq	159600gz	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3 \cdot 5^{6} \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$2280$	$48$	$0$	$1$	$1$		$1$	$1310720$	$1.793318$	$1823652903746/328593657$	$0.93527$	$3.79896$	$[0, -1, 0, -80808, 7364112]$	\(y^2=x^3-x^2-80808x+7364112\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 40.24.0-8.m.1.4, 456.24.0.?, $\ldots$	$[]$
178752.ep1	178752kg3	178752.ep	178752kg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{17} \cdot 3 \cdot 7^{14} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$3192$	$48$	$0$	$14.25370695$	$1$		$5$	$3932160$	$2.308128$	$1823652903746/328593657$	$0.93527$	$4.27418$	$[0, -1, 0, -633537, 161276865]$	\(y^2=x^3-x^2-633537x+161276865\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 28.12.0-4.c.1.1, 56.24.0-8.m.1.4, $\ldots$	$[(257, 3920), (707, 8140)]$
178752.jd1	178752ce4	178752.jd	178752ce	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{17} \cdot 3 \cdot 7^{14} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$3192$	$48$	$0$	$12.93229730$	$1$		$1$	$3932160$	$2.308128$	$1823652903746/328593657$	$0.93527$	$4.27418$	$[0, 1, 0, -633537, -161276865]$	\(y^2=x^3+x^2-633537x-161276865\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 28.12.0-4.c.1.2, 56.24.0-8.m.1.3, $\ldots$	$[(406313/4, 258871395/4)]$
181944.j1	181944d4	181944.j	181944d	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{11} \cdot 3^{7} \cdot 7^{8} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.64	2B	$456$	$48$	$0$	$1$	$16$	$2$	$1$	$14745600$	$3.010124$	$1823652903746/328593657$	$0.93527$	$4.96347$	$[0, 0, 0, -10501851, -10870348970]$	\(y^2=x^3-10501851x-10870348970\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.6, 456.48.0.?	$[]$
239400.ej1	239400ej3	239400.ej	239400ej	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3^{7} \cdot 5^{6} \cdot 7^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$2280$	$48$	$0$	$1$	$1$		$1$	$5242880$	$2.342625$	$1823652903746/328593657$	$0.93527$	$4.20679$	$[0, 0, 0, -727275, 198103750]$	\(y^2=x^3-727275x+198103750\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 120.24.0.?, 380.12.0.?, $\ldots$	$[]$
363888.r1	363888r3	363888.r	363888r	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{11} \cdot 3^{7} \cdot 7^{8} \cdot 19^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.54	2B	$456$	$48$	$0$	$1$	$1$		$3$	$29491200$	$3.010124$	$1823652903746/328593657$	$0.93527$	$4.69478$	$[0, 0, 0, -10501851, 10870348970]$	\(y^2=x^3-10501851x+10870348970\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.8, 456.48.0.?	$[]$
386232.bc1	386232bc3	386232.bc	386232bc	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{11} \cdot 3 \cdot 7^{8} \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$5016$	$48$	$0$	$1$	$1$		$1$	$6553600$	$2.187546$	$1823652903746/328593657$	$0.93527$	$3.90571$	$[0, -1, 0, -391112, 78256620]$	\(y^2=x^3-x^2-391112x+78256620\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 88.24.0.?, 456.24.0.?, $\ldots$	$[]$
424536.h1	424536h4	424536.h	424536h	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( 2^{11} \cdot 3 \cdot 7^{14} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$3192$	$48$	$0$	$9.308153622$	$1$		$1$	$88473600$	$3.433773$	$1823652903746/328593657$	$0.93527$	$5.03124$	$[0, -1, 0, -57176744, -138074633556]$	\(y^2=x^3-x^2-57176744x-138074633556\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 84.12.0.?, 168.24.0.?, $\ldots$	$[(-103139/6, 10156735/6)]$
478800.bj1	478800bj4	478800.bj	478800bj	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{11} \cdot 3^{7} \cdot 5^{6} \cdot 7^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$2280$	$48$	$0$	$3.122921430$	$1$		$5$	$10485760$	$2.342625$	$1823652903746/328593657$	$0.93527$	$3.98384$	$[0, 0, 0, -727275, -198103750]$	\(y^2=x^3-727275x-198103750\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 120.24.0.?, 380.12.0.?, $\ldots$	$[(-425, 5850)]$
485184.q1	485184q3	485184.q	485184q	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{17} \cdot 3 \cdot 7^{8} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$1$	$1$		$1$	$29491200$	$2.807392$	$1823652903746/328593657$	$0.93527$	$4.40580$	$[0, -1, 0, -4667489, 3222399969]$	\(y^2=x^3-x^2-4667489x+3222399969\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.2, 76.12.0.?, $\ldots$	$[]$
485184.fq1	485184fq4	485184.fq	485184fq	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{17} \cdot 3 \cdot 7^{8} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$456$	$48$	$0$	$8.965597014$	$1$		$1$	$29491200$	$2.807392$	$1823652903746/328593657$	$0.93527$	$4.40580$	$[0, 1, 0, -4667489, -3222399969]$	\(y^2=x^3+x^2-4667489x-3222399969\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.4, 76.12.0.?, $\ldots$	$[(-10199/3, 668440/3)]$

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