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.i4	3192a4	3192.i	3192a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 7 \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$2048$	$0.501193$	$3799448348/2736741$	$0.90028$	$3.59298$	$[0, -1, 0, 328, 1020]$	\(y^2=x^3-x^2+328x+1020\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 28.12.0-4.c.1.1, 84.24.0.?, $\ldots$	$[]$
6384.bf4	6384k4	6384.bf	6384k	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 7 \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$6.550343415$	$1$		$1$	$4096$	$0.501193$	$3799448348/2736741$	$0.90028$	$3.30873$	$[0, 1, 0, 328, -1020]$	\(y^2=x^3+x^2+328x-1020\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.2, 84.24.0.?, $\ldots$	$[(133/6, 3455/6)]$
9576.c4	9576w4	9576.c	9576w	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{7} \cdot 7 \cdot 19^{4} \)	$2$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3192$	$48$	$0$	$5.602472755$	$1$		$17$	$16384$	$1.050499$	$3799448348/2736741$	$0.90028$	$3.88145$	$[0, 0, 0, 2949, -30490]$	\(y^2=x^3+2949x-30490\)	2.3.0.a.1, 4.12.0-4.c.1.1, 84.24.0.?, 456.24.0.?, 1064.24.0.?, $\ldots$	$[(19, 180), (35, 340)]$
19152.l4	19152v4	19152.l	19152v	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{7} \cdot 7 \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3192$	$48$	$0$	$4.141325510$	$1$		$3$	$32768$	$1.050499$	$3799448348/2736741$	$0.90028$	$3.60859$	$[0, 0, 0, 2949, 30490]$	\(y^2=x^3+2949x+30490\)	2.3.0.a.1, 4.12.0-4.c.1.2, 84.24.0.?, 456.24.0.?, 1064.24.0.?, $\ldots$	$[(6, 220)]$
22344.s4	22344u3	22344.s	22344u	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 7^{7} \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3192$	$48$	$0$	$10.07022118$	$1$		$1$	$98304$	$1.474148$	$3799448348/2736741$	$0.90028$	$4.06069$	$[0, 1, 0, 16056, -381984]$	\(y^2=x^3+x^2+16056x-381984\)	2.3.0.a.1, 4.12.0-4.c.1.2, 84.24.0.?, 456.24.0.?, 1064.24.0.?, $\ldots$	$[(21277/6, 3173885/6)]$
25536.o4	25536co3	25536.o	25536co	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3 \cdot 7 \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$32768$	$0.847766$	$3799448348/2736741$	$0.90028$	$3.26655$	$[0, -1, 0, 1311, -9471]$	\(y^2=x^3-x^2+1311x-9471\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.1, 84.12.0.?, $\ldots$	$[]$
25536.cc4	25536bc3	25536.cc	25536bc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3 \cdot 7 \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$32768$	$0.847766$	$3799448348/2736741$	$0.90028$	$3.26655$	$[0, 1, 0, 1311, 9471]$	\(y^2=x^3+x^2+1311x+9471\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.2, 84.12.0.?, $\ldots$	$[]$
44688.f4	44688n3	44688.f	44688n	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 7^{7} \cdot 19^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3192$	$48$	$0$	$4.688110842$	$1$		$5$	$196608$	$1.474148$	$3799448348/2736741$	$0.90028$	$3.79782$	$[0, -1, 0, 16056, 381984]$	\(y^2=x^3-x^2+16056x+381984\)	2.3.0.a.1, 4.12.0-4.c.1.1, 84.24.0.?, 456.24.0.?, 1064.24.0.?, $\ldots$	$[(349/2, 12495/2)]$
60648.bn4	60648bi3	60648.bn	60648bi	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3 \cdot 7 \cdot 19^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3192$	$48$	$0$	$1$	$16$	$2$	$1$	$737280$	$1.973412$	$3799448348/2736741$	$0.90028$	$4.23653$	$[0, 1, 0, 118288, -7706160]$	\(y^2=x^3+x^2+118288x-7706160\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
67032.cc4	67032ce3	67032.cc	67032ce	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{7} \cdot 7^{7} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$786432$	$2.023453$	$3799448348/2736741$	$0.90028$	$4.25241$	$[0, 0, 0, 144501, 10458070]$	\(y^2=x^3+144501x+10458070\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.2, 84.24.0.?, $\ldots$	$[]$
76608.em4	76608bc3	76608.em	76608bc	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3^{7} \cdot 7 \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$262144$	$1.397072$	$3799448348/2736741$	$0.90028$	$3.53357$	$[0, 0, 0, 11796, -243920]$	\(y^2=x^3+11796x-243920\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
76608.et4	76608fm3	76608.et	76608fm	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3^{7} \cdot 7 \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$3192$	$48$	$0$	$1.349585183$	$1$		$7$	$262144$	$1.397072$	$3799448348/2736741$	$0.90028$	$3.53357$	$[0, 0, 0, 11796, 243920]$	\(y^2=x^3+11796x+243920\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 84.12.0.?, 168.24.0.?, $\ldots$	$[(37, 855)]$
79800.bw4	79800bt3	79800.bw	79800bt	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 5^{6} \cdot 7 \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$2.926044373$	$1$		$3$	$262144$	$1.305912$	$3799448348/2736741$	$0.90028$	$3.42387$	$[0, 1, 0, 8192, 143888]$	\(y^2=x^3+x^2+8192x+143888\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 84.12.0.?, 140.12.0.?, $\ldots$	$[(208, 3300)]$
121296.bo4	121296s3	121296.bo	121296s	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3 \cdot 7 \cdot 19^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3192$	$48$	$0$	$18.41126977$	$1$		$1$	$1474560$	$1.973412$	$3799448348/2736741$	$0.90028$	$3.98567$	$[0, -1, 0, 118288, 7706160]$	\(y^2=x^3-x^2+118288x+7706160\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$	$[(96171217/129, 944727528860/129)]$
134064.ff4	134064fb3	134064.ff	134064fb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{7} \cdot 7^{7} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$1572864$	$2.023453$	$3799448348/2736741$	$0.90028$	$4.00275$	$[0, 0, 0, 144501, -10458070]$	\(y^2=x^3+144501x-10458070\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 28.12.0-4.c.1.1, 84.24.0.?, $\ldots$	$[]$
159600.f4	159600gr3	159600.f	159600gr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 5^{6} \cdot 7 \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$3.548768938$	$1$		$3$	$524288$	$1.305912$	$3799448348/2736741$	$0.90028$	$3.22578$	$[0, -1, 0, 8192, -143888]$	\(y^2=x^3-x^2+8192x-143888\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 84.12.0.?, 140.12.0.?, $\ldots$	$[(117, 1550)]$
178752.eb4	178752kc3	178752.eb	178752kc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{16} \cdot 3 \cdot 7^{7} \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$3192$	$48$	$0$	$6.082518224$	$1$		$3$	$1572864$	$1.820721$	$3799448348/2736741$	$0.90028$	$3.70637$	$[0, -1, 0, 64223, -3120095]$	\(y^2=x^3-x^2+64223x-3120095\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 84.12.0.?, 168.24.0.?, $\ldots$	$[(272, 5865)]$
178752.jq4	178752cl4	178752.jq	178752cl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{16} \cdot 3 \cdot 7^{7} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$1572864$	$1.820721$	$3799448348/2736741$	$0.90028$	$3.70637$	$[0, 1, 0, 64223, 3120095]$	\(y^2=x^3+x^2+64223x+3120095\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
181944.c4	181944bi4	181944.c	181944bi	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{7} \cdot 7 \cdot 19^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$8.051858640$	$1$		$3$	$5898240$	$2.522717$	$3799448348/2736741$	$0.90028$	$4.39649$	$[0, 0, 0, 1064589, 209130910]$	\(y^2=x^3+1064589x+209130910\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 56.12.0-4.c.1.3, 76.12.0.?, $\ldots$	$[(2514, 137020)]$
239400.ct4	239400ct3	239400.ct	239400ct	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{7} \cdot 5^{6} \cdot 7 \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$2097152$	$1.855217$	$3799448348/2736741$	$0.90028$	$3.65237$	$[0, 0, 0, 73725, -3811250]$	\(y^2=x^3+73725x-3811250\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 84.12.0.?, 420.24.0.?, $\ldots$	$[]$
363888.z4	363888z3	363888.z	363888z	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{7} \cdot 7 \cdot 19^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$11796480$	$2.522717$	$3799448348/2736741$	$0.90028$	$4.15850$	$[0, 0, 0, 1064589, -209130910]$	\(y^2=x^3+1064589x-209130910\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 56.12.0-4.c.1.3, 76.12.0.?, $\ldots$	$[]$
386232.bb4	386232bb3	386232.bb	386232bb	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( - 2^{10} \cdot 3 \cdot 7 \cdot 11^{6} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$35112$	$48$	$0$	$1$	$4$	$2$	$1$	$2621440$	$1.700140$	$3799448348/2736741$	$0.90028$	$3.37191$	$[0, -1, 0, 39648, -1516260]$	\(y^2=x^3-x^2+39648x-1516260\)	2.3.0.a.1, 4.6.0.c.1, 84.12.0.?, 132.12.0.?, 308.12.0.?, $\ldots$	$[]$
424536.n4	424536n4	424536.n	424536n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( - 2^{10} \cdot 3 \cdot 7^{7} \cdot 19^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$35389440$	$2.946369$	$3799448348/2736741$	$0.90028$	$4.50134$	$[0, -1, 0, 5796096, 2654805084]$	\(y^2=x^3-x^2+5796096x+2654805084\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.5, 56.12.0-4.c.1.5, 76.12.0.?, $\ldots$	$[]$
478800.hb4	478800hb4	478800.hb	478800hb	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{7} \cdot 5^{6} \cdot 7 \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$4194304$	$1.855217$	$3799448348/2736741$	$0.90028$	$3.45881$	$[0, 0, 0, 73725, 3811250]$	\(y^2=x^3+73725x+3811250\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 84.12.0.?, 420.24.0.?, $\ldots$	$[]$
485184.n4	485184n3	485184.n	485184n	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{16} \cdot 3 \cdot 7 \cdot 19^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$11796480$	$2.319984$	$3799448348/2736741$	$0.90028$	$3.88130$	$[0, -1, 0, 473151, -62122431]$	\(y^2=x^3-x^2+473151x-62122431\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 168.24.0.?, $\ldots$	$[]$
485184.fu4	485184fu4	485184.fu	485184fu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{16} \cdot 3 \cdot 7 \cdot 19^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$3192$	$48$	$0$	$13.63974256$	$1$		$1$	$11796480$	$2.319984$	$3799448348/2736741$	$0.90028$	$3.88130$	$[0, 1, 0, 473151, 62122431]$	\(y^2=x^3+x^2+473151x+62122431\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 168.24.0.?, $\ldots$	$[(1179601/33, 1544347000/33)]$

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