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.i1	3192a3	3192.i	3192a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$2048$	$0.501193$	$202119559492/136857$	$0.90544$	$4.08552$	$[0, -1, 0, -1232, 17052]$	\(y^2=x^3-x^2-1232x+17052\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0-4.c.1.5, 76.12.0.?, $\ldots$	$[]$
6384.bf1	6384k3	6384.bf	6384k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1.637585853$	$1$		$3$	$4096$	$0.501193$	$202119559492/136857$	$0.90544$	$3.76230$	$[0, 1, 0, -1232, -17052]$	\(y^2=x^3+x^2-1232x-17052\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.5, 76.12.0.?, $\ldots$	$[(42, 84)]$
9576.c1	9576w3	9576.c	9576w	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{4} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3192$	$48$	$0$	$5.602472755$	$1$		$9$	$16384$	$1.050499$	$202119559492/136857$	$0.90544$	$4.31496$	$[0, 0, 0, -11091, -449314]$	\(y^2=x^3-11091x-449314\)	2.3.0.a.1, 4.12.0-4.c.1.2, 114.6.0.?, 168.24.0.?, 228.24.0.?, $\ldots$	$[(-61, 16), (163, 1440)]$
19152.l1	19152v3	19152.l	19152v	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3192$	$48$	$0$	$1.035331377$	$1$		$13$	$32768$	$1.050499$	$202119559492/136857$	$0.90544$	$4.01162$	$[0, 0, 0, -11091, 449314]$	\(y^2=x^3-11091x+449314\)	2.3.0.a.1, 4.12.0-4.c.1.1, 114.6.0.?, 168.24.0.?, 228.24.0.?, $\ldots$	$[(59, 18)]$
22344.s1	22344u4	22344.s	22344u	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3192$	$48$	$0$	$10.07022118$	$1$		$1$	$98304$	$1.474148$	$202119559492/136857$	$0.90544$	$4.45753$	$[0, 1, 0, -60384, -5728080]$	\(y^2=x^3+x^2-60384x-5728080\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 114.6.0.?, $\ldots$	$[(-68659/22, 610779/22)]$
25536.o1	25536co4	25536.o	25536co	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3 \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$32768$	$0.847766$	$202119559492/136857$	$0.90544$	$3.65816$	$[0, -1, 0, -4929, -131487]$	\(y^2=x^3-x^2-4929x-131487\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.4, 114.6.0.?, $\ldots$	$[]$
25536.cc1	25536bc4	25536.cc	25536bc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3 \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$32768$	$0.847766$	$202119559492/136857$	$0.90544$	$3.65816$	$[0, 1, 0, -4929, 131487]$	\(y^2=x^3+x^2-4929x+131487\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.4, 114.6.0.?, $\ldots$	$[]$
44688.f1	44688n4	44688.f	44688n	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3192$	$48$	$0$	$1.172027710$	$1$		$7$	$196608$	$1.474148$	$202119559492/136857$	$0.90544$	$4.16897$	$[0, -1, 0, -60384, 5728080]$	\(y^2=x^3-x^2-60384x+5728080\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 114.6.0.?, $\ldots$	$[(152, 196)]$
60648.bn1	60648bi4	60648.bn	60648bi	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3 \cdot 7^{4} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3192$	$48$	$0$	$1$	$16$	$2$	$1$	$737280$	$1.973412$	$202119559492/136857$	$0.90544$	$4.59738$	$[0, 1, 0, -444872, -114290688]$	\(y^2=x^3+x^2-444872x-114290688\)	2.3.0.a.1, 4.12.0-4.c.1.2, 114.6.0.?, 168.24.0.?, 228.24.0.?, $\ldots$	$[]$
67032.cc1	67032ce4	67032.cc	67032ce	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{10} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$786432$	$2.023453$	$202119559492/136857$	$0.90544$	$4.61001$	$[0, 0, 0, -543459, 154114702]$	\(y^2=x^3-543459x+154114702\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.1, 114.6.0.?, $\ldots$	$[]$
76608.em1	76608bc4	76608.em	76608bc	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{7} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$262144$	$1.397072$	$202119559492/136857$	$0.90544$	$3.88693$	$[0, 0, 0, -44364, -3594512]$	\(y^2=x^3-44364x-3594512\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 114.6.0.?, 168.24.0.?, $\ldots$	$[]$
76608.et1	76608fm4	76608.et	76608fm	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{7} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$3192$	$48$	$0$	$1.349585183$	$1$		$5$	$262144$	$1.397072$	$202119559492/136857$	$0.90544$	$3.88693$	$[0, 0, 0, -44364, 3594512]$	\(y^2=x^3-44364x+3594512\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 114.6.0.?, 168.24.0.?, $\ldots$	$[(26, 1568)]$
79800.bw1	79800bt4	79800.bw	79800bt	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$2.926044373$	$1$		$3$	$262144$	$1.305912$	$202119559492/136857$	$0.90544$	$3.77595$	$[0, 1, 0, -30808, 2069888]$	\(y^2=x^3+x^2-30808x+2069888\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 114.6.0.?, 168.12.0.?, $\ldots$	$[(112, 192)]$
121296.bo1	121296s4	121296.bo	121296s	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3 \cdot 7^{4} \cdot 19^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3192$	$48$	$0$	$4.602817444$	$1$		$5$	$1474560$	$1.973412$	$202119559492/136857$	$0.90544$	$4.32516$	$[0, -1, 0, -444872, 114290688]$	\(y^2=x^3-x^2-444872x+114290688\)	2.3.0.a.1, 4.12.0-4.c.1.1, 114.6.0.?, 168.24.0.?, 228.24.0.?, $\ldots$	$[(23136, 3517584)]$
134064.ff1	134064fb4	134064.ff	134064fb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{10} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$1572864$	$2.023453$	$202119559492/136857$	$0.90544$	$4.33935$	$[0, 0, 0, -543459, -154114702]$	\(y^2=x^3-543459x-154114702\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.2, 114.6.0.?, $\ldots$	$[]$
159600.f1	159600gr4	159600.f	159600gr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$3.548768938$	$1$		$3$	$524288$	$1.305912$	$202119559492/136857$	$0.90544$	$3.55749$	$[0, -1, 0, -30808, -2069888]$	\(y^2=x^3-x^2-30808x-2069888\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 114.6.0.?, 168.12.0.?, $\ldots$	$[(-99, 2)]$
178752.eb1	178752kc4	178752.eb	178752kc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3 \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$3192$	$48$	$0$	$6.082518224$	$1$		$1$	$1572864$	$1.820721$	$202119559492/136857$	$0.90544$	$4.03497$	$[0, -1, 0, -241537, -45583103]$	\(y^2=x^3-x^2-241537x-45583103\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 114.6.0.?, 168.24.0.?, $\ldots$	$[(-2501/3, 820/3)]$
178752.jq1	178752cl3	178752.jq	178752cl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3 \cdot 7^{10} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$1572864$	$1.820721$	$202119559492/136857$	$0.90544$	$4.03497$	$[0, 1, 0, -241537, 45583103]$	\(y^2=x^3+x^2-241537x+45583103\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 114.6.0.?, 168.24.0.?, $\ldots$	$[]$
181944.c1	181944bi3	181944.c	181944bi	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{7} \cdot 7^{4} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$2.012964660$	$1$		$5$	$5898240$	$2.522717$	$202119559492/136857$	$0.90544$	$4.72461$	$[0, 0, 0, -4003851, 3081844726]$	\(y^2=x^3-4003851x+3081844726\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0-4.c.1.3, 76.12.0.?, $\ldots$	$[(95, 51984)]$
239400.ct1	239400ct4	239400.ct	239400ct	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$2097152$	$1.855217$	$202119559492/136857$	$0.90544$	$3.97322$	$[0, 0, 0, -277275, -56164250]$	\(y^2=x^3-277275x-56164250\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 114.6.0.?, 168.12.0.?, $\ldots$	$[]$
363888.z1	363888z4	363888.z	363888z	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{7} \cdot 7^{4} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$11796480$	$2.522717$	$202119559492/136857$	$0.90544$	$4.46885$	$[0, 0, 0, -4003851, -3081844726]$	\(y^2=x^3-4003851x-3081844726\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.3, 76.12.0.?, $\ldots$	$[]$
386232.bb1	386232bb4	386232.bb	386232bb	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{10} \cdot 3 \cdot 7^{4} \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$35112$	$48$	$0$	$1$	$4$	$2$	$1$	$2621440$	$1.700140$	$202119559492/136857$	$0.90544$	$3.68083$	$[0, -1, 0, -149112, -22099812]$	\(y^2=x^3-x^2-149112x-22099812\)	2.3.0.a.1, 4.6.0.c.1, 114.6.0.?, 132.12.0.?, 168.12.0.?, $\ldots$	$[]$
424536.n1	424536n3	424536.n	424536n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( 2^{10} \cdot 3 \cdot 7^{10} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$35389440$	$2.946369$	$202119559492/136857$	$0.90544$	$4.80800$	$[0, -1, 0, -21798744, 39158108508]$	\(y^2=x^3-x^2-21798744x+39158108508\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.5, 28.12.0-4.c.1.1, 114.6.0.?, $\ldots$	$[]$
478800.hb1	478800hb3	478800.hb	478800hb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$4194304$	$1.855217$	$202119559492/136857$	$0.90544$	$3.76265$	$[0, 0, 0, -277275, 56164250]$	\(y^2=x^3-277275x+56164250\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 114.6.0.?, 168.12.0.?, $\ldots$	$[]$
485184.n1	485184n4	485184.n	485184n	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{16} \cdot 3 \cdot 7^{4} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$11796480$	$2.319984$	$202119559492/136857$	$0.90544$	$4.18484$	$[0, -1, 0, -1779489, -912546015]$	\(y^2=x^3-x^2-1779489x-912546015\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 114.6.0.?, 168.24.0.?, $\ldots$	$[]$
485184.fu1	485184fu3	485184.fu	485184fu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{16} \cdot 3 \cdot 7^{4} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$3192$	$48$	$0$	$3.409935641$	$1$		$3$	$11796480$	$2.319984$	$202119559492/136857$	$0.90544$	$4.18484$	$[0, 1, 0, -1779489, 912546015]$	\(y^2=x^3+x^2-1779489x+912546015\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 114.6.0.?, 168.24.0.?, $\ldots$	$[(-97, 32928)]$

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