Elliptic curve search results

Results (42 matches)

 

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
546.g3	546g1	546.g	546g	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.12	2B	$1$	$1$		$1$	$48$	$-0.569175$	$38272753/4368$	$[1, 0, 0, -7, -7]$	\(y^2+xy=x^3-7x-7\)
1638.d3	1638i1	1638.d	1638i	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{4} \cdot 3^{7} \cdot 7 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$0.414262525$	$1$		$9$	$384$	$-0.019868$	$38272753/4368$	$[1, -1, 0, -63, 189]$	\(y^2+xy=x^3-x^2-63x+189\)
3822.t3	3822x1	3822.t	3822x	$4$	$4$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{4} \cdot 3 \cdot 7^{7} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1$	$1$		$3$	$2304$	$0.403780$	$38272753/4368$	$[1, 1, 1, -344, 2057]$	\(y^2+xy+y=x^3+x^2-344x+2057\)
4368.k3	4368o1	4368.k	4368o	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{16} \cdot 3 \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1$	$1$		$1$	$1152$	$0.123973$	$38272753/4368$	$[0, -1, 0, -112, 448]$	\(y^2=x^3-x^2-112x+448\)
7098.j3	7098k1	7098.j	7098k	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$8064$	$0.713300$	$38272753/4368$	$[1, 0, 1, -1187, -14194]$	\(y^2+xy+y=x^3-1187x-14194\)
11466.z3	11466y1	11466.z	11466y	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{4} \cdot 3^{7} \cdot 7^{7} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$18432$	$0.953087$	$38272753/4368$	$[1, -1, 0, -3096, -58640]$	\(y^2+xy=x^3-x^2-3096x-58640\)
13104.j3	13104bt1	13104.j	13104bt	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{16} \cdot 3^{7} \cdot 7 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1.996967870$	$1$		$5$	$9216$	$0.673279$	$38272753/4368$	$[0, 0, 0, -1011, -11086]$	\(y^2=x^3-1011x-11086\)
13650.b3	13650e1	13650.b	13650e	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{4} \cdot 3 \cdot 5^{6} \cdot 7 \cdot 13 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3.234078668$	$1$		$13$	$6144$	$0.235544$	$38272753/4368$	$[1, 1, 0, -175, -875]$	\(y^2+xy=x^3+x^2-175x-875\)
17472.m3	17472o1	17472.m	17472o	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{22} \cdot 3 \cdot 7 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$4.072740421$	$1$		$1$	$9216$	$0.470546$	$38272753/4368$	$[0, -1, 0, -449, -3135]$	\(y^2=x^3-x^2-449x-3135\)
17472.bv3	17472cu1	17472.bv	17472cu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \)	\( 2^{22} \cdot 3 \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1$	$1$		$1$	$9216$	$0.470546$	$38272753/4368$	$[0, 1, 0, -449, 3135]$	\(y^2=x^3+x^2-449x+3135\)
21294.ck3	21294cg1	21294.ck	21294cg	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{4} \cdot 3^{7} \cdot 7 \cdot 13^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3.102957560$	$1$		$5$	$64512$	$1.262606$	$38272753/4368$	$[1, -1, 1, -10679, 383231]$	\(y^2+xy+y=x^3-x^2-10679x+383231\)
30576.cg3	30576dc1	30576.cg	30576dc	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{16} \cdot 3 \cdot 7^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$5.229745798$	$1$		$1$	$55296$	$1.096928$	$38272753/4368$	$[0, 1, 0, -5504, -142668]$	\(y^2=x^3+x^2-5504x-142668\)
40950.eb3	40950dy1	40950.eb	40950dy	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{4} \cdot 3^{7} \cdot 5^{6} \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$49152$	$0.784850$	$38272753/4368$	$[1, -1, 1, -1580, 22047]$	\(y^2+xy+y=x^3-x^2-1580x+22047\)
49686.u3	49686k1	49686.u	49686k	$4$	$4$	\( 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( 2^{4} \cdot 3 \cdot 7^{7} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$387072$	$1.686255$	$38272753/4368$	$[1, 1, 0, -58139, 4810317]$	\(y^2+xy=x^3+x^2-58139x+4810317\)
52416.fc3	52416fj1	52416.fc	52416fj	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{22} \cdot 3^{7} \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$73728$	$1.019852$	$38272753/4368$	$[0, 0, 0, -4044, -88688]$	\(y^2=x^3-4044x-88688\)
52416.fg3	52416dd1	52416.fg	52416dd	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 13 \)	\( 2^{22} \cdot 3^{7} \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$73728$	$1.019852$	$38272753/4368$	$[0, 0, 0, -4044, 88688]$	\(y^2=x^3-4044x+88688\)
56784.h3	56784cb1	56784.h	56784cb	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{16} \cdot 3 \cdot 7 \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1.503545507$	$1$		$3$	$193536$	$1.406446$	$38272753/4368$	$[0, -1, 0, -18984, 908400]$	\(y^2=x^3-x^2-18984x+908400\)
66066.bg3	66066w1	66066.bg	66066w	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 11^{2} \cdot 13 \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 11^{6} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$61440$	$0.629773$	$38272753/4368$	$[1, 0, 1, -850, 8468]$	\(y^2+xy+y=x^3-850x+8468\)
91728.ep3	91728fo1	91728.ep	91728fo	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{16} \cdot 3^{7} \cdot 7^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2.052300199$	$1$		$5$	$442368$	$1.646235$	$38272753/4368$	$[0, 0, 0, -49539, 3802498]$	\(y^2=x^3-49539x+3802498\)
95550.dp3	95550eb1	95550.dp	95550eb	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{4} \cdot 3 \cdot 5^{6} \cdot 7^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.114055309$	$1$		$3$	$294912$	$1.208500$	$38272753/4368$	$[1, 0, 1, -8601, 274348]$	\(y^2+xy+y=x^3-8601x+274348\)
109200.ha3	109200gl1	109200.ha	109200gl	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{16} \cdot 3 \cdot 5^{6} \cdot 7 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5.191994994$	$1$		$1$	$147456$	$0.928692$	$38272753/4368$	$[0, 1, 0, -2808, 50388]$	\(y^2=x^3+x^2-2808x+50388\)
122304.da3	122304fi1	122304.da	122304fi	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{22} \cdot 3 \cdot 7^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$6.895143860$	$1$		$1$	$442368$	$1.443501$	$38272753/4368$	$[0, -1, 0, -22017, -1119327]$	\(y^2=x^3-x^2-22017x-1119327\)
122304.hy3	122304dh1	122304.hy	122304dh	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \)	\( 2^{22} \cdot 3 \cdot 7^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$4.722507485$	$1$		$1$	$442368$	$1.443501$	$38272753/4368$	$[0, 1, 0, -22017, 1119327]$	\(y^2=x^3+x^2-22017x+1119327\)
149058.fc3	149058p1	149058.fc	149058p	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \)	\( 2^{4} \cdot 3^{7} \cdot 7^{7} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.13	2B	$1$	$1$		$1$	$3096576$	$2.235561$	$38272753/4368$	$[1, -1, 1, -523256, -130401813]$	\(y^2+xy+y=x^3-x^2-523256x-130401813\)
157794.bq3	157794x1	157794.bq	157794x	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$221184$	$0.847432$	$38272753/4368$	$[1, 1, 1, -2029, -32365]$	\(y^2+xy+y=x^3+x^2-2029x-32365\)
170352.fn3	170352cg1	170352.fn	170352cg	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{16} \cdot 3^{7} \cdot 7 \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1$	$1$		$1$	$1548288$	$1.955753$	$38272753/4368$	$[0, 0, 0, -170859, -24355942]$	\(y^2=x^3-170859x-24355942\)
177450.ht3	177450ee1	177450.ht	177450ee	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( 2^{4} \cdot 3 \cdot 5^{6} \cdot 7 \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$7.794191721$	$1$		$1$	$1032192$	$1.518019$	$38272753/4368$	$[1, 1, 1, -29663, -1774219]$	\(y^2+xy+y=x^3+x^2-29663x-1774219\)
197106.k3	197106cj1	197106.k	197106cj	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \cdot 19^{2} \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$331776$	$0.903045$	$38272753/4368$	$[1, 1, 0, -2534, 42948]$	\(y^2+xy=x^3+x^2-2534x+42948\)
198198.db3	198198k1	198198.db	198198k	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 11^{2} \cdot 13 \)	\( 2^{4} \cdot 3^{7} \cdot 7 \cdot 11^{6} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1.199110633$	$1$		$7$	$491520$	$1.179079$	$38272753/4368$	$[1, -1, 1, -7646, -228643]$	\(y^2+xy+y=x^3-x^2-7646x-228643\)
227136.df3	227136iy1	227136.df	227136iy	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{22} \cdot 3 \cdot 7 \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$12.16615825$	$1$		$1$	$1548288$	$1.753021$	$38272753/4368$	$[0, -1, 0, -75937, -7191263]$	\(y^2=x^3-x^2-75937x-7191263\)
227136.iv3	227136bu1	227136.iv	227136bu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \)	\( 2^{22} \cdot 3 \cdot 7 \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$9$	$3$	$1$	$1548288$	$1.753021$	$38272753/4368$	$[0, 1, 0, -75937, 7191263]$	\(y^2=x^3+x^2-75937x+7191263\)
286650.pw3	286650pw1	286650.pw	286650pw	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{4} \cdot 3^{7} \cdot 5^{6} \cdot 7^{7} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$2359296$	$1.757805$	$38272753/4368$	$[1, -1, 1, -77405, -7407403]$	\(y^2+xy+y=x^3-x^2-77405x-7407403\)
288834.bx3	288834bx1	288834.bx	288834bx	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \cdot 23^{2} \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \cdot 23^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$608256$	$0.998572$	$38272753/4368$	$[1, 0, 0, -3714, 77748]$	\(y^2+xy=x^3-3714x+77748\)
327600.ii3	327600ii1	327600.ii	327600ii	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{16} \cdot 3^{7} \cdot 5^{6} \cdot 7 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3.133498606$	$1$		$5$	$1179648$	$1.477997$	$38272753/4368$	$[0, 0, 0, -25275, -1385750]$	\(y^2=x^3-25275x-1385750\)
366912.cy3	366912cy1	366912.cy	366912cy	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{22} \cdot 3^{7} \cdot 7^{7} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1.291934137$	$1$		$5$	$3538944$	$1.992807$	$38272753/4368$	$[0, 0, 0, -198156, -30419984]$	\(y^2=x^3-198156x-30419984\)
366912.et3	366912et1	366912.et	366912et	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 13 \)	\( 2^{22} \cdot 3^{7} \cdot 7^{7} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$3538944$	$1.992807$	$38272753/4368$	$[0, 0, 0, -198156, 30419984]$	\(y^2=x^3-198156x+30419984\)
397488.ir3	397488ir1	397488.ir	397488ir	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \)	\( 2^{16} \cdot 3 \cdot 7^{7} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$1$		$1$	$9289728$	$2.379402$	$38272753/4368$	$[0, 1, 0, -930232, -309720748]$	\(y^2=x^3+x^2-930232x-309720748\)
436800.fz3	436800fz1	436800.fz	436800fz	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{22} \cdot 3 \cdot 5^{6} \cdot 7 \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$4.248142068$	$1$		$3$	$1179648$	$1.275265$	$38272753/4368$	$[0, -1, 0, -11233, 414337]$	\(y^2=x^3-x^2-11233x+414337\)
436800.oa3	436800oa1	436800.oa	436800oa	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( 2^{22} \cdot 3 \cdot 5^{6} \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$1179648$	$1.275265$	$38272753/4368$	$[0, 1, 0, -11233, -414337]$	\(y^2=x^3+x^2-11233x-414337\)
459186.r3	459186r1	459186.r	459186r	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13 \cdot 29^{2} \)	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1$	$4$	$2$	$1$	$1161216$	$1.114473$	$38272753/4368$	$[1, 1, 0, -5904, -158928]$	\(y^2+xy=x^3+x^2-5904x-158928\)
462462.r3	462462r1	462462.r	462462r	$4$	$4$	\( 2 \cdot 3 \cdot 7^{2} \cdot 11^{2} \cdot 13 \)	\( 2^{4} \cdot 3 \cdot 7^{7} \cdot 11^{6} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3.021740956$	$1$		$5$	$2949120$	$1.602728$	$38272753/4368$	$[1, 1, 0, -41626, -2946236]$	\(y^2+xy=x^3+x^2-41626x-2946236\)
473382.bs3	473382bs1	473382.bs	473382bs	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 2^{4} \cdot 3^{7} \cdot 7 \cdot 13 \cdot 17^{6} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5.362342512$	$1$		$9$	$1769472$	$1.396738$	$38272753/4368$	$[1, -1, 0, -18261, 855589]$	\(y^2+xy=x^3-x^2-18261x+855589\)