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.m4	3192i1	3192.m	3192i	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1064$	$48$	$0$	$2.365087787$	$1$		$7$	$512$	$-0.004390$	$464857088/410571$	$0.88297$	$2.81714$	$[0, 1, 0, 41, 86]$	\(y^2=x^3+x^2+41x+86\)	2.3.0.a.1, 4.12.0-4.c.1.1, 38.6.0.b.1, 56.24.0-56.ba.1.4, 76.24.0.?, $\ldots$	$[(14, 60)]$
6384.f4	6384c1	6384.f	6384c	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1064$	$48$	$0$	$1$	$1$		$1$	$1024$	$-0.004390$	$464857088/410571$	$0.88297$	$2.59427$	$[0, -1, 0, 41, -86]$	\(y^2=x^3-x^2+41x-86\)	2.3.0.a.1, 4.12.0-4.c.1.2, 38.6.0.b.1, 56.24.0-56.ba.1.12, 76.24.0.?, $\ldots$	$[]$
9576.x4	9576z1	9576.x	9576z	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{8} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$4096$	$0.544916$	$464857088/410571$	$0.88297$	$3.19859$	$[0, 0, 0, 366, -1955]$	\(y^2=x^3+366x-1955\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[]$
19152.bk4	19152r1	19152.bk	19152r	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{8} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$6.149061763$	$1$		$1$	$8192$	$0.544916$	$464857088/410571$	$0.88297$	$2.97373$	$[0, 0, 0, 366, 1955]$	\(y^2=x^3+366x+1955\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[(-95/8, 19215/8)]$
22344.m4	22344i1	22344.m	22344i	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1064$	$48$	$0$	$2.330829775$	$1$		$3$	$24576$	$0.968565$	$464857088/410571$	$0.88297$	$3.43561$	$[0, -1, 0, 1993, -25500]$	\(y^2=x^3-x^2+1993x-25500\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.2, 38.6.0.b.1, $\ldots$	$[(75, 735)]$
25536.bp4	25536u1	25536.bp	25536u	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1064$	$48$	$0$	$1.348026480$	$1$		$5$	$8192$	$0.342184$	$464857088/410571$	$0.88297$	$2.64970$	$[0, -1, 0, 163, 525]$	\(y^2=x^3-x^2+163x+525\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 38.6.0.b.1, 56.24.0-56.ba.1.11, $\ldots$	$[(4, 35)]$
25536.db4	25536ct1	25536.db	25536ct	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1064$	$48$	$0$	$3.764300608$	$1$		$1$	$8192$	$0.342184$	$464857088/410571$	$0.88297$	$2.64970$	$[0, 1, 0, 163, -525]$	\(y^2=x^3+x^2+163x-525\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 38.6.0.b.1, 56.24.0-56.ba.1.3, $\ldots$	$[(37/2, 345/2)]$
44688.dn4	44688bb1	44688.dn	44688bb	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1064$	$48$	$0$	$7.539289928$	$1$		$1$	$49152$	$0.968565$	$464857088/410571$	$0.88297$	$3.21321$	$[0, 1, 0, 1993, 25500]$	\(y^2=x^3+x^2+1993x+25500\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.1, 38.6.0.b.1, $\ldots$	$[(2833/4, 156255/4)]$
60648.e4	60648ba1	60648.e	60648ba	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{4} \cdot 19^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1064$	$48$	$0$	$1$	$1$		$3$	$184320$	$1.467829$	$464857088/410571$	$0.88297$	$3.66812$	$[0, -1, 0, 14681, -501536]$	\(y^2=x^3-x^2+14681x-501536\)	2.3.0.a.1, 4.12.0-4.c.1.1, 38.6.0.b.1, 56.24.0-56.ba.1.13, 76.24.0.?, $\ldots$	$[]$
67032.w4	67032cs1	67032.w	67032cs	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{4} \cdot 3^{8} \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$4.291014256$	$1$		$3$	$196608$	$1.517872$	$464857088/410571$	$0.88297$	$3.68912$	$[0, 0, 0, 17934, 670565]$	\(y^2=x^3+17934x+670565\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[(109, 1980)]$
76608.be4	76608dz1	76608.be	76608dz	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{8} \cdot 7^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$4.038136600$	$1$		$3$	$65536$	$0.891490$	$464857088/410571$	$0.88297$	$2.97697$	$[0, 0, 0, 1464, 15640]$	\(y^2=x^3+1464x+15640\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[(774, 21560)]$
76608.bh4	76608cp1	76608.bh	76608cp	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{8} \cdot 7^{4} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$4.482764518$	$1$		$11$	$65536$	$0.891490$	$464857088/410571$	$0.88297$	$2.97697$	$[0, 0, 0, 1464, -15640]$	\(y^2=x^3+1464x-15640\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[(73, 693), (17, 119)]$
79800.b4	79800z1	79800.b	79800z	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5320$	$48$	$0$	$1.568963043$	$1$		$19$	$65536$	$0.800329$	$464857088/410571$	$0.88297$	$2.86929$	$[0, -1, 0, 1017, 8712]$	\(y^2=x^3-x^2+1017x+8712\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[(-3, 75), (12, 150)]$
121296.ce4	121296bb1	121296.ce	121296bb	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{4} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1064$	$48$	$0$	$10.09988119$	$1$		$1$	$368640$	$1.467829$	$464857088/410571$	$0.88297$	$3.45092$	$[0, 1, 0, 14681, 501536]$	\(y^2=x^3+x^2+14681x+501536\)	2.3.0.a.1, 4.12.0-4.c.1.2, 38.6.0.b.1, 56.24.0-56.ba.1.5, 76.24.0.?, $\ldots$	$[(12257/16, 4699695/16)]$
134064.ba4	134064dt1	134064.ba	134064dt	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{4} \cdot 3^{8} \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$7.071377760$	$1$		$1$	$393216$	$1.517872$	$464857088/410571$	$0.88297$	$3.47253$	$[0, 0, 0, 17934, -670565]$	\(y^2=x^3+17934x-670565\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[(2081/4, 125775/4)]$
159600.gt4	159600fq1	159600.gt	159600fq	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{2} \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5320$	$48$	$0$	$1$	$1$		$1$	$131072$	$0.800329$	$464857088/410571$	$0.88297$	$2.70328$	$[0, 1, 0, 1017, -8712]$	\(y^2=x^3+x^2+1017x-8712\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[]$
178752.t4	178752dg1	178752.t	178752dg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{2} \cdot 7^{10} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1064$	$48$	$0$	$1$	$1$		$1$	$393216$	$1.315140$	$464857088/410571$	$0.88297$	$3.18877$	$[0, -1, 0, 7971, 196029]$	\(y^2=x^3-x^2+7971x+196029\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 38.6.0.b.1, 56.24.0-56.ba.1.1, $\ldots$	$[]$
178752.gv4	178752gg1	178752.gv	178752gg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{2} \cdot 7^{10} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1064$	$48$	$0$	$1.584019907$	$4$	$2$	$5$	$393216$	$1.315140$	$464857088/410571$	$0.88297$	$3.18877$	$[0, 1, 0, 7971, -196029]$	\(y^2=x^3+x^2+7971x-196029\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 38.6.0.b.1, 56.24.0-56.ba.1.9, $\ldots$	$[(51, 588)]$
181944.cc4	181944cc1	181944.cc	181944cc	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{8} \cdot 7^{4} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$1474560$	$2.017136$	$464857088/410571$	$0.88297$	$3.87964$	$[0, 0, 0, 132126, 13409345]$	\(y^2=x^3+132126x+13409345\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[]$
239400.by4	239400by1	239400.by	239400by	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$524288$	$1.349636$	$464857088/410571$	$0.88297$	$3.14698$	$[0, 0, 0, 9150, -244375]$	\(y^2=x^3+9150x-244375\)	2.3.0.a.1, 4.6.0.c.1, 38.6.0.b.1, 56.12.0.ba.1, 60.12.0-4.c.1.2, $\ldots$	$[]$
363888.dp4	363888dp1	363888.dp	363888dp	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{8} \cdot 7^{4} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$19.22945922$	$1$		$1$	$2949120$	$2.017136$	$464857088/410571$	$0.88297$	$3.66963$	$[0, 0, 0, 132126, -13409345]$	\(y^2=x^3+132126x-13409345\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 38.6.0.b.1, 56.12.0.ba.1, $\ldots$	$[(526507505/832, 13222681459785/832)]$
386232.bq4	386232bq1	386232.bq	386232bq	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{4} \cdot 11^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$11704$	$48$	$0$	$1.903068253$	$1$		$5$	$655360$	$1.194557$	$464857088/410571$	$0.88297$	$2.88531$	$[0, 1, 0, 4921, -94734]$	\(y^2=x^3+x^2+4921x-94734\)	2.3.0.a.1, 4.6.0.c.1, 38.6.0.b.1, 44.12.0-4.c.1.2, 56.12.0.ba.1, $\ldots$	$[(67, 735)]$
424536.dx4	424536dx1	424536.dx	424536dx	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{2} \cdot 7^{10} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.14	2B	$1064$	$48$	$0$	$10.46303483$	$1$		$1$	$8847360$	$2.440784$	$464857088/410571$	$0.88297$	$4.01828$	$[0, 1, 0, 719353, 170588130]$	\(y^2=x^3+x^2+719353x+170588130\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 28.12.0-4.c.1.2, 38.6.0.b.1, $\ldots$	$[(-9983/8, 3783585/8)]$
478800.iy4	478800iy1	478800.iy	478800iy	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{4} \cdot 3^{8} \cdot 5^{6} \cdot 7^{4} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$1048576$	$1.349636$	$464857088/410571$	$0.88297$	$2.98020$	$[0, 0, 0, 9150, 244375]$	\(y^2=x^3+9150x+244375\)	2.3.0.a.1, 4.6.0.c.1, 38.6.0.b.1, 56.12.0.ba.1, 60.12.0-4.c.1.1, $\ldots$	$[]$
485184.di4	485184di1	485184.di	485184di	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1064$	$48$	$0$	$3.212060399$	$1$		$3$	$2949120$	$1.814404$	$464857088/410571$	$0.88297$	$3.40318$	$[0, -1, 0, 58723, 3953565]$	\(y^2=x^3-x^2+58723x+3953565\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 38.6.0.b.1, 56.24.0-56.ba.1.14, $\ldots$	$[(1837, 79420)]$
485184.is4	485184is1	485184.is	485184is	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{2} \cdot 7^{4} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1064$	$48$	$0$	$1$	$4$	$2$	$1$	$2949120$	$1.814404$	$464857088/410571$	$0.88297$	$3.40318$	$[0, 1, 0, 58723, -3953565]$	\(y^2=x^3+x^2+58723x-3953565\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 38.6.0.b.1, 56.24.0-56.ba.1.6, $\ldots$	$[]$

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