Elliptic curve search results

Results (29 matches)

  Download displayed columns for results to

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
663.b1	663c2	663.b	663c	$2$	$2$	\( 3 \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$884$	$12$	$0$	$0.204192024$	$1$		$10$	$128$	$0.129896$	$104154702625/24649677$	$0.90385$	$3.90488$	$[1, 0, 0, -98, 279]$	\(y^2+xy=x^3-98x+279\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(1, 13)]$
1989.d1	1989a2	1989.d	1989a	$2$	$2$	\( 3^{2} \cdot 13 \cdot 17 \)	\( 3^{14} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$0$	$1024$	$0.679203$	$104154702625/24649677$	$0.90385$	$4.20792$	$[1, -1, 0, -882, -7533]$	\(y^2+xy=x^3-x^2-882x-7533\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$
8619.j1	8619j2	8619.j	8619j	$2$	$2$	\( 3 \cdot 13^{2} \cdot 17 \)	\( 3^{8} \cdot 13^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.480603891$	$1$		$4$	$21504$	$1.412371$	$104154702625/24649677$	$0.90385$	$4.49791$	$[1, 0, 1, -16566, 629527]$	\(y^2+xy+y=x^3-16566x+629527\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-13, 924)]$
10608.h1	10608o2	10608.h	10608o	$2$	$2$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.376869513$	$1$		$7$	$8192$	$0.823044$	$104154702625/24649677$	$0.90385$	$3.63422$	$[0, -1, 0, -1568, -17856]$	\(y^2=x^3-x^2-1568x-17856\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-14, 34)]$
11271.b1	11271a2	11271.b	11271a	$2$	$2$	\( 3 \cdot 13 \cdot 17^{2} \)	\( 3^{8} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$2.772723454$	$1$		$2$	$36864$	$1.546503$	$104154702625/24649677$	$0.90385$	$4.54110$	$[1, 1, 1, -28328, 1399052]$	\(y^2+xy+y=x^3+x^2-28328x+1399052\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(239, 2770)]$
16575.g1	16575b2	16575.g	16575b	$2$	$2$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 5^{6} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$0$	$18432$	$0.934615$	$104154702625/24649677$	$0.90385$	$3.60509$	$[1, 1, 0, -2450, 34875]$	\(y^2+xy=x^3+x^2-2450x+34875\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$
25857.g1	25857f2	25857.g	25857f	$2$	$2$	\( 3^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{14} \cdot 13^{7} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$0$	$172032$	$1.961678$	$104154702625/24649677$	$0.90385$	$4.66033$	$[1, -1, 1, -149090, -16997236]$	\(y^2+xy+y=x^3-x^2-149090x-16997236\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$
31824.t1	31824r2	31824.t	31824r	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{14} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.215211072$	$1$		$7$	$65536$	$1.372351$	$104154702625/24649677$	$0.90385$	$3.88490$	$[0, 0, 0, -14115, 496226]$	\(y^2=x^3-14115x+496226\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(337, 5832)]$
32487.b1	32487g2	32487.b	32487g	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 7^{6} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.892332799$	$1$		$4$	$46080$	$1.102852$	$104154702625/24649677$	$0.90385$	$3.56589$	$[1, 1, 1, -4803, -100500]$	\(y^2+xy+y=x^3+x^2-4803x-100500\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-35, 179)]$
33813.k1	33813e2	33813.k	33813e	$2$	$2$	\( 3^{2} \cdot 13 \cdot 17^{2} \)	\( 3^{14} \cdot 13 \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$0$	$294912$	$2.095810$	$104154702625/24649677$	$0.90385$	$4.69479$	$[1, -1, 0, -254952, -38029361]$	\(y^2+xy=x^3-x^2-254952x-38029361\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$
42432.m1	42432l2	42432.m	42432l	$2$	$2$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{8} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$3.115943302$	$1$		$5$	$65536$	$1.169617$	$104154702625/24649677$	$0.90385$	$3.55171$	$[0, -1, 0, -6273, 149121]$	\(y^2=x^3-x^2-6273x+149121\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(80, 391)]$
42432.bv1	42432ck2	42432.bv	42432ck	$2$	$2$	\( 2^{6} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{8} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.830403660$	$1$		$5$	$65536$	$1.169617$	$104154702625/24649677$	$0.90385$	$3.55171$	$[0, 1, 0, -6273, -149121]$	\(y^2=x^3+x^2-6273x-149121\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-27, 36)]$
49725.i1	49725q2	49725.i	49725q	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{14} \cdot 5^{6} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$0$	$147456$	$1.483921$	$104154702625/24649677$	$0.90385$	$3.84838$	$[1, -1, 1, -22055, -963678]$	\(y^2+xy+y=x^3-x^2-22055x-963678\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$
80223.m1	80223o2	80223.m	80223o	$2$	$2$	\( 3 \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 11^{6} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$0$	$179200$	$1.328844$	$104154702625/24649677$	$0.90385$	$3.52059$	$[1, 0, 1, -11861, -383209]$	\(y^2+xy+y=x^3-11861x-383209\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$
97461.t1	97461v2	97461.t	97461v	$2$	$2$	\( 3^{2} \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{14} \cdot 7^{6} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$4.749373430$	$1$		$2$	$368640$	$1.652157$	$104154702625/24649677$	$0.90385$	$3.79868$	$[1, -1, 0, -43227, 2670268]$	\(y^2+xy=x^3-x^2-43227x+2670268\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-232, 530)]$
127296.br1	127296u2	127296.br	127296u	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{14} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$4.694015636$	$1$		$3$	$524288$	$1.718924$	$104154702625/24649677$	$0.90385$	$3.78054$	$[0, 0, 0, -56460, -3969808]$	\(y^2=x^3-56460x-3969808\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-172, 808)]$
127296.cm1	127296cn2	127296.cm	127296cn	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{14} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$524288$	$1.718924$	$104154702625/24649677$	$0.90385$	$3.78054$	$[0, 0, 0, -56460, 3969808]$	\(y^2=x^3-56460x+3969808\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$
137904.r1	137904bk2	137904.r	137904bk	$2$	$2$	\( 2^{4} \cdot 3 \cdot 13^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 13^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$2.825667970$	$1$		$5$	$1376256$	$2.105518$	$104154702625/24649677$	$0.90385$	$4.14698$	$[0, -1, 0, -265048, -40289744]$	\(y^2=x^3-x^2-265048x-40289744\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-238, 3042)]$
146523.u1	146523bb2	146523.u	146523bb	$2$	$2$	\( 3 \cdot 13^{2} \cdot 17^{2} \)	\( 3^{8} \cdot 13^{7} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$9.694000073$	$1$		$0$	$6193152$	$2.828979$	$104154702625/24649677$	$0.90385$	$4.85569$	$[1, 1, 0, -4787435, 3097654812]$	\(y^2+xy=x^3+x^2-4787435x+3097654812\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(9807557/28, 30129805523/28)]$
180336.ck1	180336l2	180336.ck	180336l	$2$	$2$	\( 2^{4} \cdot 3 \cdot 13 \cdot 17^{2} \)	\( 2^{12} \cdot 3^{8} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.208445447$	$1$		$7$	$2359296$	$2.239651$	$104154702625/24649677$	$0.90385$	$4.18805$	$[0, 1, 0, -453248, -90445836]$	\(y^2=x^3+x^2-453248x-90445836\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-380, 5202)]$
215475.m1	215475u2	215475.m	215475u	$2$	$2$	\( 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{8} \cdot 5^{6} \cdot 13^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.726157098$	$1$		$4$	$3096576$	$2.217091$	$104154702625/24649677$	$0.90385$	$4.10529$	$[1, 1, 1, -414138, 78690906]$	\(y^2+xy+y=x^3+x^2-414138x+78690906\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(590, 6042)]$
239343.e1	239343e2	239343.e	239343e	$2$	$2$	\( 3 \cdot 13 \cdot 17 \cdot 19^{2} \)	\( 3^{8} \cdot 13 \cdot 17^{2} \cdot 19^{6} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$17.72346032$	$1$		$0$	$921600$	$1.602116$	$104154702625/24649677$	$0.90385$	$3.47465$	$[1, 1, 0, -35385, -1984428]$	\(y^2+xy=x^3+x^2-35385x-1984428\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(847/2, 1319/2), (-273/2, 3027/2)]$
240669.o1	240669o2	240669.o	240669o	$2$	$2$	\( 3^{2} \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 3^{14} \cdot 11^{6} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$3.785960677$	$1$		$2$	$1433600$	$1.878151$	$104154702625/24649677$	$0.90385$	$3.74042$	$[1, -1, 1, -106745, 10346636]$	\(y^2+xy+y=x^3-x^2-106745x+10346636\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-366, 718)]$
265200.ew1	265200ew2	265200.ew	265200ew	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 5^{6} \cdot 13 \cdot 17^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.573926533$	$1$		$21$	$1179648$	$1.627762$	$104154702625/24649677$	$0.90385$	$3.47075$	$[0, 1, 0, -39208, -2310412]$	\(y^2=x^3+x^2-39208x-2310412\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-82, 600), (-106, 816)]$
281775.bw1	281775bw2	281775.bw	281775bw	$2$	$2$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( 3^{8} \cdot 5^{6} \cdot 13 \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$2.951939695$	$1$		$2$	$5308416$	$2.351223$	$104154702625/24649677$	$0.90385$	$4.14580$	$[1, 0, 1, -708201, 176297923]$	\(y^2+xy+y=x^3-708201x+176297923\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(41, 12117)]$
350727.f1	350727f2	350727.f	350727f	$2$	$2$	\( 3 \cdot 13 \cdot 17 \cdot 23^{2} \)	\( 3^{8} \cdot 13 \cdot 17^{2} \cdot 23^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.245484168$	$1$		$6$	$1441792$	$1.697643$	$104154702625/24649677$	$0.90385$	$3.46044$	$[1, 0, 0, -51853, -3498292]$	\(y^2+xy=x^3-51853x-3498292\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-163, 875)]$
413712.co1	413712co2	413712.co	413712co	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{14} \cdot 13^{7} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$2.470531998$	$1$		$7$	$11010048$	$2.654823$	$104154702625/24649677$	$0.90385$	$4.30438$	$[0, 0, 0, -2385435, 1090208522]$	\(y^2=x^3-2385435x+1090208522\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(493, 5832)]$
422331.bm1	422331bm2	422331.bm	422331bm	$2$	$2$	\( 3 \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{8} \cdot 7^{6} \cdot 13^{7} \cdot 17^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$12.21697675$	$1$		$4$	$7741440$	$2.385326$	$104154702625/24649677$	$0.90385$	$4.04787$	$[1, 1, 0, -811710, -216739557]$	\(y^2+xy=x^3+x^2-811710x-216739557\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-658, 6075), (-1557/2, 52425/2)]$
439569.v1	439569v2	439569.v	439569v	$2$	$2$	\( 3^{2} \cdot 13^{2} \cdot 17^{2} \)	\( 3^{14} \cdot 13^{7} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$0$	$49545216$	$3.378284$	$104154702625/24649677$	$0.90385$	$4.95244$	$[1, -1, 1, -43086920, -83679766842]$	\(y^2+xy+y=x^3-x^2-43086920x-83679766842\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[ ]$

  Download displayed columns for results to