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
2730.x6	2730x6	2730.x	2730x	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.48.0.176	2B	$4368$	$192$	$1$	$0.487726598$	$1$		$6$	$49152$	$2.003269$	$293623352309352854879/187320324116835000$	$1.02562$	$5.95658$	$[1, 1, 1, 138470, -6288673]$	\(y^2+xy+y=x^3+x^2+138470x-6288673\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.1.3, 56.96.0-56.bn.1.4, 624.96.0.?, $\ldots$	$[(87, 2491)]$
8190.i6	8190n6	8190.i	8190n	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{14} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$1$	$1$		$0$	$393216$	$2.552578$	$293623352309352854879/187320324116835000$	$1.02562$	$5.96188$	$[1, -1, 0, 1246230, 171040396]$	\(y^2+xy=x^3-x^2+1246230x+171040396\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 12.12.0-4.c.1.1, 24.48.0-8.bb.1.1, $\ldots$	$[ ]$
13650.x6	13650z6	13650.x	13650z	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{10} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$1$	$1$		$0$	$1179648$	$2.807991$	$293623352309352854879/187320324116835000$	$1.02562$	$5.96392$	$[1, 0, 1, 3461749, -793007602]$	\(y^2+xy+y=x^3+3461749x-793007602\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 20.12.0-4.c.1.1, 40.48.0-8.bb.1.8, $\ldots$	$[ ]$
19110.cn6	19110cp6	19110.cn	19110cp	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{4} \cdot 7^{7} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.216	2B	$4368$	$192$	$1$	$1$	$1$		$0$	$2359296$	$2.976227$	$293623352309352854879/187320324116835000$	$1.02562$	$5.96515$	$[1, 0, 0, 6785029, 2177369865]$	\(y^2+xy=x^3+6785029x+2177369865\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.1.4, 28.12.0-4.c.1.1, 56.96.0-56.bn.1.8, $\ldots$	$[ ]$
21840.cc6	21840cg5	21840.cc	21840cg	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$1$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.159	2B	$4368$	$192$	$1$	$4.480433826$	$1$		$11$	$1179648$	$2.696419$	$293623352309352854879/187320324116835000$	$1.02562$	$5.54938$	$[0, 1, 0, 2215520, 406906100]$	\(y^2=x^3+x^2+2215520x+406906100\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 56.96.0-56.bn.1.3, 624.96.0.?, $\ldots$	$[(-145, 9090)]$
35490.d6	35490a5	35490.d	35490a	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{4} \cdot 7 \cdot 13^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$13.88509453$	$1$		$0$	$8257536$	$3.285744$	$293623352309352854879/187320324116835000$	$1.02562$	$5.96721$	$[1, 1, 0, 23401427, -13933221323]$	\(y^2+xy=x^3+x^2+23401427x-13933221323\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 48.48.0-8.bb.1.8, 52.12.0-4.c.1.1, $\ldots$	$[(1952593/43, 8652454882/43)]$
40950.dy6	40950ds5	40950.dy	40950ds	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{3} \cdot 3^{14} \cdot 5^{10} \cdot 7 \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$7.074532289$	$1$		$2$	$9437184$	$3.357296$	$293623352309352854879/187320324116835000$	$1.02562$	$5.96765$	$[1, -1, 1, 31155745, 21411205247]$	\(y^2+xy+y=x^3-x^2+31155745x+21411205247\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 56.48.0.bn.1, 60.12.0-4.c.1.1, $\ldots$	$[(5329, 579360)]$
57330.cr6	57330ci5	57330.cr	57330ci	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{14} \cdot 5^{4} \cdot 7^{7} \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$0$	$18874368$	$3.525532$	$293623352309352854879/187320324116835000$	$1.02562$	$5.96865$	$[1, -1, 0, 61065261, -58788986355]$	\(y^2+xy=x^3-x^2+61065261x-58788986355\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 24.48.0-8.bb.1.3, 56.48.0.bn.1, $\ldots$	$[ ]$
65520.e6	65520cv5	65520.e	65520cv	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{14} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$9437184$	$3.245724$	$293623352309352854879/187320324116835000$	$1.02562$	$5.59402$	$[0, 0, 0, 19939677, -10966525022]$	\(y^2=x^3+19939677x-10966525022\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 12.12.0-4.c.1.2, 24.48.0-8.bb.1.2, $\ldots$	$[ ]$
87360.b6	87360ec5	87360.b	87360ec	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{8} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.219	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$9437184$	$3.042992$	$293623352309352854879/187320324116835000$	$1.02562$	$5.23876$	$[0, -1, 0, 8862079, 3246386721]$	\(y^2=x^3-x^2+8862079x+3246386721\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.1.7, 28.12.0-4.c.1.2, 56.96.0-56.bn.1.2, $\ldots$	$[ ]$
87360.ff6	87360ck5	87360.ff	87360ck	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{8} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.215	2B	$4368$	$192$	$1$	$4.013748881$	$1$		$3$	$9437184$	$3.042992$	$293623352309352854879/187320324116835000$	$1.02562$	$5.23876$	$[0, 1, 0, 8862079, -3246386721]$	\(y^2=x^3+x^2+8862079x-3246386721\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.1.5, 28.12.0-4.c.1.1, 56.96.0-56.bn.1.1, $\ldots$	$[(1419, 110400)]$
95550.m6	95550bt5	95550.m	95550bt	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{10} \cdot 7^{7} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$1.547875967$	$1$		$6$	$56623104$	$3.780945$	$293623352309352854879/187320324116835000$	$1.02562$	$5.97004$	$[1, 1, 0, 169625725, 272171233125]$	\(y^2+xy=x^3+x^2+169625725x+272171233125\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 40.48.0-8.bb.1.6, 56.48.0.bn.1, $\ldots$	$[(1165, 685980)]$
106470.ex6	106470fi5	106470.ex	106470fi	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{14} \cdot 5^{4} \cdot 7 \cdot 13^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.98	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$0$	$66060288$	$3.835052$	$293623352309352854879/187320324116835000$	$1.02562$	$5.97032$	$[1, -1, 1, 210612838, 376407588561]$	\(y^2+xy+y=x^3-x^2+210612838x+376407588561\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 16.48.0-8.bb.1.8, 56.48.0.bn.1, $\ldots$	$[ ]$
109200.dm6	109200ds5	109200.dm	109200ds	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{8} \cdot 5^{10} \cdot 7 \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$19.00499507$	$1$		$1$	$28311552$	$3.501137$	$293623352309352854879/187320324116835000$	$1.02562$	$5.61189$	$[0, -1, 0, 55387992, 50752486512]$	\(y^2=x^3-x^2+55387992x+50752486512\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 20.12.0-4.c.1.2, 40.48.0-8.bb.1.7, $\ldots$	$[(1485469554/545, 108931049314758/545)]$
152880.ci6	152880ez5	152880.ci	152880ez	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 7^{7} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.220	2B	$4368$	$192$	$1$	$5.537165645$	$1$		$1$	$56623104$	$3.669373$	$293623352309352854879/187320324116835000$	$1.02562$	$5.62283$	$[0, -1, 0, 108560464, -139351671360]$	\(y^2=x^3-x^2+108560464x-139351671360\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.bb.1.2, 28.12.0-4.c.1.2, 56.96.0-56.bn.1.7, $\ldots$	$[(13912/3, 4841200/3)]$
177450.kh6	177450bi5	177450.kh	177450bi	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{10} \cdot 7 \cdot 13^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$0$	$198180864$	$4.090462$	$293623352309352854879/187320324116835000$	$1.02562$	$5.97158$	$[1, 0, 0, 585035662, -1742822736708]$	\(y^2+xy=x^3+585035662x-1742822736708\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 56.48.0.bn.1, 240.48.0.?, $\ldots$	$[ ]$
248430.fd6	248430fd6	248430.fd	248430fd	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{4} \cdot 7^{7} \cdot 13^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$1$	$1$		$0$	$396361728$	$4.258698$	$293623352309352854879/187320324116835000$	$1.02562$	$5.97235$	$[1, 0, 1, 1146669897, 4782534923506]$	\(y^2+xy+y=x^3+1146669897x+4782534923506\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 48.48.0-8.bb.1.7, 56.48.0.bn.1, $\ldots$	$[ ]$
262080.kc6	262080kc5	262080.kc	262080kc	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{14} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$1$	$75497472$	$3.592297$	$293623352309352854879/187320324116835000$	$1.02562$	$5.30579$	$[0, 0, 0, 79758708, -87732200176]$	\(y^2=x^3+79758708x-87732200176\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 24.48.0-8.bb.1.5, 56.48.0.bn.1, $\ldots$	$[ ]$
262080.ku6	262080ku6	262080.ku	262080ku	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{14} \cdot 5^{4} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$1$	$75497472$	$3.592297$	$293623352309352854879/187320324116835000$	$1.02562$	$5.30579$	$[0, 0, 0, 79758708, 87732200176]$	\(y^2=x^3+79758708x+87732200176\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 24.48.0-8.bb.1.6, 56.48.0.bn.1, $\ldots$	$[ ]$
283920.fl6	283920fl6	283920.fl	283920fl	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 7 \cdot 13^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$198180864$	$3.978893$	$293623352309352854879/187320324116835000$	$1.02562$	$5.64143$	$[0, 1, 0, 374422824, 892475010324]$	\(y^2=x^3+x^2+374422824x+892475010324\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 48.48.0-8.bb.1.6, 52.12.0-4.c.1.2, $\ldots$	$[ ]$
286650.qs6	286650qs5	286650.qs	286650qs	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{14} \cdot 5^{10} \cdot 7^{7} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$2.285661216$	$1$		$0$	$452984832$	$4.330254$	$293623352309352854879/187320324116835000$	$1.02562$	$5.97266$	$[1, -1, 1, 1526631520, -7347096662853]$	\(y^2+xy+y=x^3-x^2+1526631520x-7347096662853\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 56.48.0.bn.1, 120.48.0.?, $\ldots$	$[(302891/2, 186019605/2)]$
327600.hm6	327600hm5	327600.hm	327600hm	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{15} \cdot 3^{14} \cdot 5^{10} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$1$	$226492416$	$4.050446$	$293623352309352854879/187320324116835000$	$1.02562$	$5.64547$	$[0, 0, 0, 498491925, -1370815627750]$	\(y^2=x^3+498491925x-1370815627750\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 56.48.0.bn.1, 60.12.0-4.c.1.2, $\ldots$	$[ ]$
330330.bc6	330330bc6	330330.bc	330330bc	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13 \)	\( - 2^{3} \cdot 3^{8} \cdot 5^{4} \cdot 7 \cdot 11^{6} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$48048$	$192$	$1$	$2.796299599$	$4$	$2$	$4$	$62914560$	$3.202217$	$293623352309352854879/187320324116835000$	$1.02562$	$4.84080$	$[1, 1, 0, 16754868, 8453997864]$	\(y^2+xy=x^3+x^2+16754868x+8453997864\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 44.12.0-4.c.1.1, 56.48.0.bn.1, $\ldots$	$[(1953, 219546)]$
436800.fb6	436800fb5	436800.fb	436800fb	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{8} \cdot 5^{10} \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$1$	$226492416$	$3.847710$	$293623352309352854879/187320324116835000$	$1.02562$	$5.33309$	$[0, -1, 0, 221551967, -406241444063]$	\(y^2=x^3-x^2+221551967x-406241444063\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 40.48.0-8.bb.1.3, 56.48.0.bn.1, $\ldots$	$[ ]$
436800.qi6	436800qi6	436800.qi	436800qi	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{21} \cdot 3^{8} \cdot 5^{10} \cdot 7 \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$21840$	$192$	$1$	$2.532199994$	$1$		$5$	$226492416$	$3.847710$	$293623352309352854879/187320324116835000$	$1.02562$	$5.33309$	$[0, 1, 0, 221551967, 406241444063]$	\(y^2=x^3+x^2+221551967x+406241444063\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 40.48.0-8.bb.1.4, 56.48.0.bn.1, $\ldots$	$[(-1222, 365625)]$
458640.ib6	458640ib6	458640.ib	458640ib	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{15} \cdot 3^{14} \cdot 5^{4} \cdot 7^{7} \cdot 13^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$4368$	$192$	$1$	$3.758958325$	$1$		$5$	$452984832$	$4.218681$	$293623352309352854879/187320324116835000$	$1.02562$	$5.65462$	$[0, 0, 0, 977044173, 3761518082546]$	\(y^2=x^3+977044173x+3761518082546\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 24.48.0-8.bb.1.4, 56.48.0.bn.1, $\ldots$	$[(24767, 6569030)]$

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