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.b3	3192c4	3192.b	3192c	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1064$	$48$	$0$	$1$	$1$		$1$	$24576$	$1.814154$	$-28104147578308/21301741002339$	$1.05261$	$5.58683$	$[0, -1, 0, -6384, 7110684]$	\(y^2=x^3-x^2-6384x+7110684\)	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.?, $\ldots$	$[ ]$
6384.v3	6384n4	6384.v	6384n	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{12} \cdot 19 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1064$	$48$	$0$	$2.209406959$	$1$		$9$	$49152$	$1.814154$	$-28104147578308/21301741002339$	$1.05261$	$5.14484$	$[0, 1, 0, -6384, -7110684]$	\(y^2=x^3+x^2-6384x-7110684\)	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.?, $\ldots$	$[(210, 924)]$
9576.t3	9576v4	9576.t	9576v	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{10} \cdot 7^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$16$	$2$	$1$	$196608$	$2.363461$	$-28104147578308/21301741002339$	$1.05261$	$5.63634$	$[0, 0, 0, -57459, -191931010]$	\(y^2=x^3-57459x-191931010\)	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, $\ldots$	$[ ]$
19152.bq3	19152u4	19152.bq	19152u	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{10} \cdot 7^{12} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1.438827442$	$1$		$7$	$393216$	$2.363461$	$-28104147578308/21301741002339$	$1.05261$	$5.24012$	$[0, 0, 0, -57459, 191931010]$	\(y^2=x^3-57459x+191931010\)	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, $\ldots$	$[(-267, 13720)]$
22344.bb3	22344t3	22344.bb	22344t	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{18} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1064$	$48$	$0$	$13.46734830$	$1$		$1$	$1179648$	$2.787109$	$-28104147578308/21301741002339$	$1.05261$	$5.66711$	$[0, 1, 0, -312832, -2438338960]$	\(y^2=x^3+x^2-312832x-2438338960\)	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, $\ldots$	$[(1605917/2, 2035095315/2)]$
25536.bk3	25536cm3	25536.bk	25536cm	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3^{4} \cdot 7^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1064$	$48$	$0$	$1$	$1$		$1$	$393216$	$2.160728$	$-28104147578308/21301741002339$	$1.05261$	$4.85183$	$[0, -1, 0, -25537, -56859935]$	\(y^2=x^3-x^2-25537x-56859935\)	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, $\ldots$	$[ ]$
25536.dh3	25536bb3	25536.dh	25536bb	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3^{4} \cdot 7^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1064$	$48$	$0$	$1$	$4$	$2$	$1$	$393216$	$2.160728$	$-28104147578308/21301741002339$	$1.05261$	$4.85183$	$[0, 1, 0, -25537, 56859935]$	\(y^2=x^3+x^2-25537x+56859935\)	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, $\ldots$	$[ ]$
44688.bm3	44688m3	44688.bm	44688m	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{18} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1064$	$48$	$0$	$6.920372498$	$1$		$1$	$2359296$	$2.787109$	$-28104147578308/21301741002339$	$1.05261$	$5.30025$	$[0, -1, 0, -312832, 2438338960]$	\(y^2=x^3-x^2-312832x+2438338960\)	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, $\ldots$	$[(-6080/3, 1306340/3)]$
60648.w3	60648bk3	60648.w	60648bk	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{12} \cdot 19^{7} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1064$	$48$	$0$	$31.92223628$	$1$		$5$	$8847360$	$3.286373$	$-28104147578308/21301741002339$	$1.05261$	$5.69729$	$[0, 1, 0, -2304744, -48758353344]$	\(y^2=x^3+x^2-2304744x-48758353344\)	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.?, $\ldots$	$[(4224, 129960), (590784/5, 452321448/5)]$
67032.v3	67032ch3	67032.v	67032ch	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{10} \cdot 7^{18} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$9437184$	$3.336414$	$-28104147578308/21301741002339$	$1.05261$	$5.70002$	$[0, 0, 0, -2815491, 65832336430]$	\(y^2=x^3-2815491x+65832336430\)	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, $\ldots$	$[ ]$
76608.t3	76608bk3	76608.t	76608bk	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3^{10} \cdot 7^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$3145728$	$2.710033$	$-28104147578308/21301741002339$	$1.05261$	$4.96399$	$[0, 0, 0, -229836, -1535448080]$	\(y^2=x^3-229836x-1535448080\)	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, $\ldots$	$[ ]$
76608.bw3	76608fu3	76608.bw	76608fu	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( - 2^{16} \cdot 3^{10} \cdot 7^{12} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$3.996320495$	$1$		$3$	$3145728$	$2.710033$	$-28104147578308/21301741002339$	$1.05261$	$4.96399$	$[0, 0, 0, -229836, 1535448080]$	\(y^2=x^3-229836x+1535448080\)	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, $\ldots$	$[(1916, 90160)]$
79800.bm3	79800bu3	79800.bm	79800bu	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 7^{12} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5320$	$48$	$0$	$0.615713594$	$1$		$9$	$3145728$	$2.618874$	$-28104147578308/21301741002339$	$1.05261$	$4.84912$	$[0, 1, 0, -159608, 888516288]$	\(y^2=x^3+x^2-159608x+888516288\)	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, $\ldots$	$[(208, 29400)]$
121296.n3	121296v3	121296.n	121296v	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{12} \cdot 19^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1064$	$48$	$0$	$2.924006815$	$1$		$9$	$17694720$	$3.286373$	$-28104147578308/21301741002339$	$1.05261$	$5.35994$	$[0, -1, 0, -2304744, 48758353344]$	\(y^2=x^3-x^2-2304744x+48758353344\)	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.?, $\ldots$	$[(-1336, 222376)]$
134064.z3	134064ds3	134064.z	134064ds	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{10} \cdot 7^{18} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$18874368$	$3.336414$	$-28104147578308/21301741002339$	$1.05261$	$5.36537$	$[0, 0, 0, -2815491, -65832336430]$	\(y^2=x^3-2815491x-65832336430\)	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, $\ldots$	$[ ]$
159600.bo3	159600gy3	159600.bo	159600gy	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 7^{12} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5320$	$48$	$0$	$4.750781669$	$1$		$3$	$6291456$	$2.618874$	$-28104147578308/21301741002339$	$1.05261$	$4.56857$	$[0, -1, 0, -159608, -888516288]$	\(y^2=x^3-x^2-159608x-888516288\)	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, $\ldots$	$[(2822, 145350)]$
178752.bk3	178752ir3	178752.bk	178752ir	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{16} \cdot 3^{4} \cdot 7^{18} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1064$	$48$	$0$	$33.67337886$	$1$		$1$	$18874368$	$3.133682$	$-28104147578308/21301741002339$	$1.05261$	$5.03658$	$[0, -1, 0, -1251329, -19505460351]$	\(y^2=x^3-x^2-1251329x-19505460351\)	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, $\ldots$	$[(511947588434539/411723, 4550797696715131558780/411723)]$
178752.gf3	178752o4	178752.gf	178752o	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( - 2^{16} \cdot 3^{4} \cdot 7^{18} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1064$	$48$	$0$	$1$	$4$	$2$	$1$	$18874368$	$3.133682$	$-28104147578308/21301741002339$	$1.05261$	$5.03658$	$[0, 1, 0, -1251329, 19505460351]$	\(y^2=x^3+x^2-1251329x+19505460351\)	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, $\ldots$	$[ ]$
181944.bv3	181944ce4	181944.bv	181944ce	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{10} \cdot 7^{12} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$56.91332695$	$1$		$1$	$70778880$	$3.835678$	$-28104147578308/21301741002339$	$1.05261$	$5.72475$	$[0, 0, 0, -20742699, 1316454797590]$	\(y^2=x^3-20742699x+1316454797590\)	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, $\ldots$	$[(12673483841472729208445585/19998280504, 45582259178911017240714359820548629305/19998280504)]$
239400.ef3	239400ef3	239400.ef	239400ef	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{10} \cdot 5^{6} \cdot 7^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$25165824$	$3.168179$	$-28104147578308/21301741002339$	$1.05261$	$4.95120$	$[0, 0, 0, -1436475, -23991376250]$	\(y^2=x^3-1436475x-23991376250\)	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, $\ldots$	$[ ]$
363888.ea3	363888ea3	363888.ea	363888ea	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{10} \cdot 7^{12} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$141557760$	$3.835678$	$-28104147578308/21301741002339$	$1.05261$	$5.41486$	$[0, 0, 0, -20742699, -1316454797590]$	\(y^2=x^3-20742699x-1316454797590\)	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, $\ldots$	$[ ]$
386232.j3	386232j3	386232.j	386232j	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{12} \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$11704$	$48$	$0$	$1$	$1$		$1$	$31457280$	$3.013103$	$-28104147578308/21301741002339$	$1.05261$	$4.62245$	$[0, -1, 0, -772504, -9461230436]$	\(y^2=x^3-x^2-772504x-9461230436\)	2.3.0.a.1, 4.6.0.c.1, 38.6.0.b.1, 44.12.0-4.c.1.1, 56.12.0.ba.1, $\ldots$	$[ ]$
424536.bm3	424536bm4	424536.bm	424536bm	$4$	$4$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( - 2^{10} \cdot 3^{4} \cdot 7^{18} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.14	2B	$1064$	$48$	$0$	$1$	$9$	$3$	$1$	$424673280$	$4.259331$	$-28104147578308/21301741002339$	$1.05261$	$5.74275$	$[0, -1, 0, -112932472, 16723889332060]$	\(y^2=x^3-x^2-112932472x+16723889332060\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 28.12.0-4.c.1.1, 38.6.0.b.1, $\ldots$	$[ ]$
478800.ba3	478800ba4	478800.ba	478800ba	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{10} \cdot 3^{10} \cdot 5^{6} \cdot 7^{12} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$15960$	$48$	$0$	$1$	$1$		$1$	$50331648$	$3.168179$	$-28104147578308/21301741002339$	$1.05261$	$4.68881$	$[0, 0, 0, -1436475, 23991376250]$	\(y^2=x^3-1436475x+23991376250\)	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, $\ldots$	$[ ]$
485184.do3	485184do3	485184.do	485184do	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{16} \cdot 3^{4} \cdot 7^{12} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1064$	$48$	$0$	$1$	$1$		$1$	$141557760$	$3.632946$	$-28104147578308/21301741002339$	$1.05261$	$5.11005$	$[0, -1, 0, -9218977, -390057607775]$	\(y^2=x^3-x^2-9218977x-390057607775\)	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, $\ldots$	$[ ]$
485184.ij3	485184ij4	485184.ij	485184ij	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( - 2^{16} \cdot 3^{4} \cdot 7^{12} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1064$	$48$	$0$	$4.905093081$	$1$		$1$	$141557760$	$3.632946$	$-28104147578308/21301741002339$	$1.05261$	$5.11005$	$[0, 1, 0, -9218977, 390057607775]$	\(y^2=x^3+x^2-9218977x+390057607775\)	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, $\ldots$	$[(29117/2, 6734805/2)]$

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