Elliptic curve search results

Results (22 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
1106.e4	1106e1	1106.e	1106e	$4$	$4$	\( 2 \cdot 7 \cdot 79 \)	\( - 2^{12} \cdot 7^{2} \cdot 79 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.50	2B	$632$	$48$	$0$	$1.534449056$	$1$		$11$	$192$	$0.070193$	$23076099423/15855616$	$0.91115$	$3.40473$	$[1, -1, 1, 59, 61]$	\(y^2+xy+y=x^3-x^2+59x+61\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 158.6.0.?, 316.24.0.?, $\ldots$	$[(1, 10)]$
7742.k4	7742j1	7742.k	7742j	$4$	$4$	\( 2 \cdot 7^{2} \cdot 79 \)	\( - 2^{12} \cdot 7^{8} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$4424$	$48$	$0$	$2.345672562$	$1$		$5$	$9216$	$1.043148$	$23076099423/15855616$	$0.91115$	$3.96872$	$[1, -1, 1, 2906, -26827]$	\(y^2+xy+y=x^3-x^2+2906x-26827\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 28.12.0-4.c.1.2, 56.24.0-8.p.1.3, $\ldots$	$[(41, 379)]$
8848.b4	8848c1	8848.b	8848c	$4$	$4$	\( 2^{4} \cdot 7 \cdot 79 \)	\( - 2^{24} \cdot 7^{2} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.60	2B	$632$	$48$	$0$	$2.809979183$	$1$		$5$	$4608$	$0.763340$	$23076099423/15855616$	$0.91115$	$3.54094$	$[0, 0, 0, 949, -4870]$	\(y^2=x^3+949x-4870\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.3, 158.6.0.?, 316.24.0.?, $\ldots$	$[(7, 46)]$
9954.a4	9954a1	9954.a	9954a	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 79 \)	\( - 2^{12} \cdot 3^{6} \cdot 7^{2} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1896$	$48$	$0$	$2.798280313$	$1$		$3$	$6144$	$0.619498$	$23076099423/15855616$	$0.91115$	$3.30813$	$[1, -1, 0, 534, -2188]$	\(y^2+xy=x^3-x^2+534x-2188\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.2, 24.24.0-8.p.1.8, $\ldots$	$[(29, 178)]$
27650.g4	27650a1	27650.g	27650a	$4$	$4$	\( 2 \cdot 5^{2} \cdot 7 \cdot 79 \)	\( - 2^{12} \cdot 5^{6} \cdot 7^{2} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$3160$	$48$	$0$	$1.148511434$	$1$		$7$	$24576$	$0.874911$	$23076099423/15855616$	$0.91115$	$3.27735$	$[1, -1, 0, 1483, 9141]$	\(y^2+xy=x^3-x^2+1483x+9141\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 20.12.0-4.c.1.2, 40.24.0-8.p.1.1, $\ldots$	$[(-1, 88)]$
35392.j4	35392n1	35392.j	35392n	$4$	$4$	\( 2^{6} \cdot 7 \cdot 79 \)	\( - 2^{30} \cdot 7^{2} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.101	2B	$632$	$48$	$0$	$6.307170363$	$1$		$3$	$36864$	$1.109913$	$23076099423/15855616$	$0.91115$	$3.46934$	$[0, 0, 0, 3796, -38960]$	\(y^2=x^3+3796x-38960\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.5, 158.6.0.?, 316.12.0.?, $\ldots$	$[(1068, 34960)]$
35392.m4	35392g1	35392.m	35392g	$4$	$4$	\( 2^{6} \cdot 7 \cdot 79 \)	\( - 2^{30} \cdot 7^{2} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.103	2B	$632$	$48$	$0$	$1$	$4$	$2$	$1$	$36864$	$1.109913$	$23076099423/15855616$	$0.91115$	$3.46934$	$[0, 0, 0, 3796, 38960]$	\(y^2=x^3+3796x+38960\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 158.6.0.?, 316.12.0.?, $\ldots$	$[ ]$
61936.r4	61936r1	61936.r	61936r	$4$	$4$	\( 2^{4} \cdot 7^{2} \cdot 79 \)	\( - 2^{24} \cdot 7^{8} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$4424$	$48$	$0$	$1$	$4$	$2$	$1$	$221184$	$1.736296$	$23076099423/15855616$	$0.91115$	$3.97461$	$[0, 0, 0, 46501, 1670410]$	\(y^2=x^3+46501x+1670410\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 28.12.0-4.c.1.1, 56.24.0-8.p.1.4, $\ldots$	$[ ]$
69678.i4	69678j1	69678.i	69678j	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 79 \)	\( - 2^{12} \cdot 3^{6} \cdot 7^{8} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$13272$	$48$	$0$	$7.673896863$	$1$		$1$	$294912$	$1.592453$	$23076099423/15855616$	$0.91115$	$3.77785$	$[1, -1, 0, 26157, 698165]$	\(y^2+xy=x^3-x^2+26157x+698165\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 84.12.0.?, 158.6.0.?, $\ldots$	$[(6617/8, 1059617/8)]$
79632.y4	79632v1	79632.y	79632v	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 79 \)	\( - 2^{24} \cdot 3^{6} \cdot 7^{2} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1896$	$48$	$0$	$1$	$1$		$1$	$147456$	$1.312645$	$23076099423/15855616$	$0.91115$	$3.43561$	$[0, 0, 0, 8541, 131490]$	\(y^2=x^3+8541x+131490\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.1, 24.24.0-8.p.1.6, $\ldots$	$[ ]$
87374.l4	87374j1	87374.l	87374j	$4$	$4$	\( 2 \cdot 7 \cdot 79^{2} \)	\( - 2^{12} \cdot 7^{2} \cdot 79^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.51	2B	$632$	$48$	$0$	$6.351578075$	$1$		$5$	$1198080$	$2.254917$	$23076099423/15855616$	$0.91115$	$4.40138$	$[1, -1, 1, 370169, -37609729]$	\(y^2+xy+y=x^3-x^2+370169x-37609729\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.8, 158.6.0.?, 316.24.0.?, $\ldots$	$[(2411, 120718)]$
133826.e4	133826x1	133826.e	133826x	$4$	$4$	\( 2 \cdot 7 \cdot 11^{2} \cdot 79 \)	\( - 2^{12} \cdot 7^{2} \cdot 11^{6} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$6952$	$48$	$0$	$2.154602917$	$1$		$5$	$245760$	$1.269140$	$23076099423/15855616$	$0.91115$	$3.24030$	$[1, -1, 0, 7177, -103075]$	\(y^2+xy=x^3-x^2+7177x-103075\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 44.12.0-4.c.1.2, 88.24.0.?, $\ldots$	$[(25, 290)]$
186914.b4	186914g1	186914.b	186914g	$4$	$4$	\( 2 \cdot 7 \cdot 13^{2} \cdot 79 \)	\( - 2^{12} \cdot 7^{2} \cdot 13^{6} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$8216$	$48$	$0$	$3.901902696$	$1$		$1$	$442368$	$1.352667$	$23076099423/15855616$	$0.91115$	$3.23368$	$[1, -1, 0, 10024, 164672]$	\(y^2+xy=x^3-x^2+10024x+164672\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 52.12.0-4.c.1.2, 104.24.0.?, $\ldots$	$[(-139/4, 18023/4)]$
193550.p4	193550co1	193550.p	193550co	$4$	$4$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 79 \)	\( - 2^{12} \cdot 5^{6} \cdot 7^{8} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$22120$	$48$	$0$	$1$	$1$		$1$	$1179648$	$1.847866$	$23076099423/15855616$	$0.91115$	$3.71257$	$[1, -1, 0, 72658, -3280684]$	\(y^2+xy=x^3-x^2+72658x-3280684\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 140.12.0.?, 158.6.0.?, $\ldots$	$[ ]$
221200.bj4	221200v1	221200.bj	221200v	$4$	$4$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 79 \)	\( - 2^{24} \cdot 5^{6} \cdot 7^{2} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$3160$	$48$	$0$	$1$	$1$		$1$	$589824$	$1.568058$	$23076099423/15855616$	$0.91115$	$3.39945$	$[0, 0, 0, 23725, -608750]$	\(y^2=x^3+23725x-608750\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 20.12.0-4.c.1.1, 40.24.0-8.p.1.3, $\ldots$	$[ ]$
247744.x4	247744x1	247744.x	247744x	$4$	$4$	\( 2^{6} \cdot 7^{2} \cdot 79 \)	\( - 2^{30} \cdot 7^{8} \cdot 79 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$4424$	$48$	$0$	$29.00196249$	$1$		$7$	$1769472$	$2.082867$	$23076099423/15855616$	$0.91115$	$3.86583$	$[0, 0, 0, 186004, 13363280]$	\(y^2=x^3+186004x+13363280\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0-8.p.1.1, 158.6.0.?, $\ldots$	$[(28, 4312), (15772, 1981496)]$
247744.ba4	247744ba1	247744.ba	247744ba	$4$	$4$	\( 2^{6} \cdot 7^{2} \cdot 79 \)	\( - 2^{30} \cdot 7^{8} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$4424$	$48$	$0$	$1$	$4$	$2$	$1$	$1769472$	$2.082867$	$23076099423/15855616$	$0.91115$	$3.86583$	$[0, 0, 0, 186004, -13363280]$	\(y^2=x^3+186004x-13363280\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0-8.p.1.2, 158.6.0.?, $\ldots$	$[ ]$
248850.es4	248850es1	248850.es	248850es	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 79 \)	\( - 2^{12} \cdot 3^{6} \cdot 5^{6} \cdot 7^{2} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$9480$	$48$	$0$	$0.913032226$	$1$		$9$	$786432$	$1.424217$	$23076099423/15855616$	$0.91115$	$3.22830$	$[1, -1, 1, 13345, -260153]$	\(y^2+xy+y=x^3-x^2+13345x-260153\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 60.12.0-4.c.1.2, 120.24.0.?, $\ldots$	$[(179, 2710)]$
318528.v4	318528v1	318528.v	318528v	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 79 \)	\( - 2^{30} \cdot 3^{6} \cdot 7^{2} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1896$	$48$	$0$	$1$	$1$		$1$	$1179648$	$1.659220$	$23076099423/15855616$	$0.91115$	$3.38796$	$[0, 0, 0, 34164, 1051920]$	\(y^2=x^3+34164x+1051920\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 24.24.0-8.p.1.7, 158.6.0.?, $\ldots$	$[ ]$
318528.ba4	318528ba1	318528.ba	318528ba	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 79 \)	\( - 2^{30} \cdot 3^{6} \cdot 7^{2} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$1896$	$48$	$0$	$5.765756748$	$1$		$1$	$1179648$	$1.659220$	$23076099423/15855616$	$0.91115$	$3.38796$	$[0, 0, 0, 34164, -1051920]$	\(y^2=x^3+34164x-1051920\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 24.24.0-8.p.1.5, 158.6.0.?, $\ldots$	$[(241/2, 8855/2)]$
319634.u4	319634u1	319634.u	319634u	$4$	$4$	\( 2 \cdot 7 \cdot 17^{2} \cdot 79 \)	\( - 2^{12} \cdot 7^{2} \cdot 17^{6} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$10744$	$48$	$0$	$3.372027319$	$1$		$5$	$983040$	$1.486799$	$23076099423/15855616$	$0.91115$	$3.22379$	$[1, -1, 1, 17141, 369563]$	\(y^2+xy+y=x^3-x^2+17141x+369563\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 68.12.0-4.c.1.2, 136.24.0.?, $\ldots$	$[(-13, 386)]$
399266.d4	399266d1	399266.d	399266d	$4$	$4$	\( 2 \cdot 7 \cdot 19^{2} \cdot 79 \)	\( - 2^{12} \cdot 7^{2} \cdot 19^{6} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$12008$	$48$	$0$	$1$	$1$		$1$	$1327104$	$1.542412$	$23076099423/15855616$	$0.91115$	$3.21993$	$[1, -1, 0, 21412, -527280]$	\(y^2+xy=x^3-x^2+21412x-527280\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 76.12.0.?, 152.24.0.?, $\ldots$	$[ ]$

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