Elliptic curve search results

Results (24 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
678.e1	678d2	678.e	678d	$2$	$7$	\( 2 \cdot 3 \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$4746$	$96$	$2$	$1$	$1$		$0$	$3528$	$1.644447$	$-39934705050538129/2823126576537804$	$1.05538$	$6.60201$	$1$	$[1, 0, 0, -7121, -2567403]$	\(y^2+xy=x^3-7121x-2567403\)	7.48.0-7.a.2.2, 678.2.0.?, 4746.96.2.?	$[ ]$	$1$
2034.d1	2034c2	2034.d	2034c	$2$	$7$	\( 2 \cdot 3^{2} \cdot 113 \)	\( - 2^{2} \cdot 3^{7} \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$4746$	$96$	$2$	$1$	$1$		$0$	$28224$	$2.193752$	$-39934705050538129/2823126576537804$	$1.05538$	$6.51519$	$1$	$[1, -1, 0, -64089, 69319881]$	\(y^2+xy=x^3-x^2-64089x+69319881\)	7.24.0.a.2, 21.48.0-7.a.2.2, 678.2.0.?, 1582.48.0.?, 4746.96.2.?	$[ ]$	$1$
5424.e1	5424l2	5424.e	5424l	$2$	$7$	\( 2^{4} \cdot 3 \cdot 113 \)	\( - 2^{14} \cdot 3 \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$9492$	$96$	$2$	$0.596718100$	$1$		$0$	$84672$	$2.337593$	$-39934705050538129/2823126576537804$	$1.05538$	$5.97275$	$1$	$[0, -1, 0, -113936, 164313792]$	\(y^2=x^3-x^2-113936x+164313792\)	7.24.0.a.2, 28.48.0-7.a.2.1, 678.2.0.?, 4746.48.2.?, 9492.96.2.?	$[(4456/3, 408608/3)]$	$1$
16272.w1	16272y2	16272.w	16272y	$2$	$7$	\( 2^{4} \cdot 3^{2} \cdot 113 \)	\( - 2^{14} \cdot 3^{7} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$9492$	$96$	$2$	$11.56928355$	$1$		$0$	$677376$	$2.886902$	$-39934705050538129/2823126576537804$	$1.05538$	$5.97584$	$1$	$[0, 0, 0, -1025427, -4435446958]$	\(y^2=x^3-1025427x-4435446958\)	7.24.0.a.2, 84.48.0.?, 678.2.0.?, 3164.48.0.?, 4746.48.2.?, $\ldots$	$[(1610593/13, 2027144592/13)]$	$1$
16950.b1	16950e2	16950.b	16950e	$2$	$7$	\( 2 \cdot 3 \cdot 5^{2} \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 5^{6} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$23730$	$96$	$2$	$13.94459624$	$1$		$0$	$493920$	$2.449165$	$-39934705050538129/2823126576537804$	$1.05538$	$5.41138$	$1$	$[1, 1, 0, -178025, -320925375]$	\(y^2+xy=x^3+x^2-178025x-320925375\)	7.24.0.a.2, 35.48.0-7.a.2.1, 678.2.0.?, 4746.48.2.?, 23730.96.2.?	$[(1555126/11, 1929664243/11)]$	$1$
21696.u1	21696h2	21696.u	21696h	$2$	$7$	\( 2^{6} \cdot 3 \cdot 113 \)	\( - 2^{20} \cdot 3 \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$18984$	$96$	$2$	$1$	$1$		$0$	$677376$	$2.684170$	$-39934705050538129/2823126576537804$	$1.05538$	$5.56002$	$1$	$[0, -1, 0, -455745, -1314054591]$	\(y^2=x^3-x^2-455745x-1314054591\)	7.24.0.a.2, 56.48.0-7.a.2.1, 678.2.0.?, 4746.48.2.?, 18984.96.2.?	$[ ]$	$1$
21696.bv1	21696by2	21696.bv	21696by	$2$	$7$	\( 2^{6} \cdot 3 \cdot 113 \)	\( - 2^{20} \cdot 3 \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$18984$	$96$	$2$	$1$	$1$		$0$	$677376$	$2.684170$	$-39934705050538129/2823126576537804$	$1.05538$	$5.56002$	$1$	$[0, 1, 0, -455745, 1314054591]$	\(y^2=x^3+x^2-455745x+1314054591\)	7.24.0.a.2, 56.48.0-7.a.2.2, 678.2.0.?, 4746.48.2.?, 18984.96.2.?	$[ ]$	$1$
33222.r1	33222p2	33222.r	33222p	$2$	$7$	\( 2 \cdot 3 \cdot 7^{2} \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 7^{6} \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.2	7B.1.4	$4746$	$96$	$2$	$1$	$1$		$0$	$1333584$	$2.617401$	$-39934705050538129/2823126576537804$	$1.05538$	$5.25551$	$1$	$[1, 1, 1, -348930, 880270299]$	\(y^2+xy+y=x^3+x^2-348930x+880270299\)	7.48.0-7.a.2.1, 678.2.0.?, 4746.96.2.?	$[ ]$	$1$
50850.y1	50850bd2	50850.y	50850bd	$2$	$7$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 113 \)	\( - 2^{2} \cdot 3^{7} \cdot 5^{6} \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$23730$	$96$	$2$	$1$	$1$		$0$	$3951360$	$2.998474$	$-39934705050538129/2823126576537804$	$1.05538$	$5.47105$	$1$	$[1, -1, 1, -1602230, 8663382897]$	\(y^2+xy+y=x^3-x^2-1602230x+8663382897\)	7.24.0.a.2, 105.48.0.?, 678.2.0.?, 4746.48.2.?, 7910.48.0.?, $\ldots$	$[ ]$	$1$
65088.bo1	65088dg2	65088.bo	65088dg	$2$	$7$	\( 2^{6} \cdot 3^{2} \cdot 113 \)	\( - 2^{20} \cdot 3^{7} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$18984$	$96$	$2$	$16.56520581$	$1$		$0$	$5419008$	$3.233475$	$-39934705050538129/2823126576537804$	$1.05538$	$5.60363$	$1$	$[0, 0, 0, -4101708, -35483575664]$	\(y^2=x^3-4101708x-35483575664\)	7.24.0.a.2, 168.48.0.?, 678.2.0.?, 4746.48.2.?, 6328.48.0.?, $\ldots$	$[(103364444/95, 1021641265872/95)]$	$1$
65088.bv1	65088ba2	65088.bv	65088ba	$2$	$7$	\( 2^{6} \cdot 3^{2} \cdot 113 \)	\( - 2^{20} \cdot 3^{7} \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$18984$	$96$	$2$	$1$	$1$		$0$	$5419008$	$3.233475$	$-39934705050538129/2823126576537804$	$1.05538$	$5.60363$	$1$	$[0, 0, 0, -4101708, 35483575664]$	\(y^2=x^3-4101708x+35483575664\)	7.24.0.a.2, 168.48.0.?, 678.2.0.?, 4746.48.2.?, 6328.48.0.?, $\ldots$	$[ ]$	$1$
76614.k1	76614j2	76614.k	76614j	$2$	$7$	\( 2 \cdot 3 \cdot 113^{2} \)	\( - 2^{2} \cdot 3 \cdot 113^{13} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$4746$	$96$	$2$	$1$	$49$	$7$	$0$	$45045504$	$4.008141$	$-39934705050538129/2823126576537804$	$1.05538$	$6.34896$	$1$	$[1, 1, 1, -90928315, -3703679732491]$	\(y^2+xy+y=x^3+x^2-90928315x-3703679732491\)	7.24.0.a.2, 42.48.0-7.a.2.2, 678.2.0.?, 791.48.0.?, 4746.96.2.?	$[ ]$	$1$
82038.e1	82038e2	82038.e	82038e	$2$	$7$	\( 2 \cdot 3 \cdot 11^{2} \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 11^{6} \cdot 113^{7} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$52206$	$96$	$2$	$2.772068492$	$1$		$4$	$4939200$	$2.843395$	$-39934705050538129/2823126576537804$	$1.05538$	$5.07531$	$1$	$[1, 0, 1, -861644, 3416351750]$	\(y^2+xy+y=x^3-861644x+3416351750\)	7.24.0.a.2, 77.48.0.?, 678.2.0.?, 4746.48.2.?, 52206.96.2.?	$[(-1477, 39045), (1641725/17, 2081129325/17)]$	$1$
99666.k1	99666i2	99666.k	99666i	$2$	$7$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 113 \)	\( - 2^{2} \cdot 3^{7} \cdot 7^{6} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$4746$	$96$	$2$	$16.02296820$	$1$		$0$	$10668672$	$3.166710$	$-39934705050538129/2823126576537804$	$1.05538$	$5.32657$	$1$	$[1, -1, 0, -3140370, -23770438448]$	\(y^2+xy=x^3-x^2-3140370x-23770438448\)	7.24.0.a.2, 21.48.0-7.a.2.1, 678.2.0.?, 1582.48.0.?, 4746.96.2.?	$[(23536526/85, 13564954646/85)]$	$1$
114582.h1	114582f2	114582.h	114582f	$2$	$7$	\( 2 \cdot 3 \cdot 13^{2} \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 13^{6} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$61698$	$96$	$2$	$8.330943004$	$1$		$2$	$6223392$	$2.926922$	$-39934705050538129/2823126576537804$	$1.05538$	$5.01579$	$1$	$[1, 0, 1, -1203453, -5639380940]$	\(y^2+xy+y=x^3-1203453x-5639380940\)	7.24.0.a.2, 91.48.0.?, 678.2.0.?, 4746.48.2.?, 61698.96.2.?	$[(4645, 296000)]$	$1$
135600.cg1	135600t2	135600.cg	135600t	$2$	$7$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 113 \)	\( - 2^{14} \cdot 3 \cdot 5^{6} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$47460$	$96$	$2$	$26.57049635$	$1$		$0$	$11854080$	$3.142315$	$-39934705050538129/2823126576537804$	$1.05538$	$5.16303$	$1$	$[0, 1, 0, -2848408, 20533527188]$	\(y^2=x^3+x^2-2848408x+20533527188\)	7.24.0.a.2, 140.48.0.?, 678.2.0.?, 4746.48.2.?, 47460.96.2.?	$[(1380506144326/17227, 1679850167241646128/17227)]$	$1$
195942.t1	195942p2	195942.t	195942p	$2$	$7$	\( 2 \cdot 3 \cdot 17^{2} \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 17^{6} \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$80682$	$96$	$2$	$1$	$49$	$7$	$0$	$17781120$	$3.061054$	$-39934705050538129/2823126576537804$	$1.05538$	$4.92704$	$1$	$[1, 1, 1, -2057975, -12611592967]$	\(y^2+xy+y=x^3+x^2-2057975x-12611592967\)	7.24.0.a.2, 119.48.0.?, 678.2.0.?, 4746.48.2.?, 80682.96.2.?	$[ ]$	$1$
229842.i1	229842q2	229842.i	229842q	$2$	$7$	\( 2 \cdot 3^{2} \cdot 113^{2} \)	\( - 2^{2} \cdot 3^{7} \cdot 113^{13} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$4746$	$96$	$2$	$1$	$4$	$2$	$0$	$360364032$	$4.557449$	$-39934705050538129/2823126576537804$	$1.05538$	$6.31791$	$1$	$[1, -1, 0, -818354835, 99998534422417]$	\(y^2+xy=x^3-x^2-818354835x+99998534422417\)	7.24.0.a.2, 14.48.0-7.a.2.1, 678.2.0.?, 2373.48.0.?, 4746.96.2.?	$[ ]$	$1$
244758.e1	244758e2	244758.e	244758e	$2$	$7$	\( 2 \cdot 3 \cdot 19^{2} \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 19^{6} \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$90174$	$96$	$2$	$1$	$1$		$0$	$23115456$	$3.116665$	$-39934705050538129/2823126576537804$	$1.05538$	$4.89249$	$1$	$[1, 1, 0, -2570688, 17604675804]$	\(y^2+xy=x^3+x^2-2570688x+17604675804\)	7.24.0.a.2, 133.48.0.?, 678.2.0.?, 4746.48.2.?, 90174.96.2.?	$[ ]$	$1$
246114.o1	246114o2	246114.o	246114o	$2$	$7$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 113 \)	\( - 2^{2} \cdot 3^{7} \cdot 11^{6} \cdot 113^{7} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$52206$	$96$	$2$	$37.93249970$	$1$		$4$	$39513600$	$3.392700$	$-39934705050538129/2823126576537804$	$1.05538$	$5.15715$	$1$	$[1, -1, 1, -7754792, -92241497257]$	\(y^2+xy+y=x^3-x^2-7754792x-92241497257\)	7.24.0.a.2, 231.48.0.?, 678.2.0.?, 4746.48.2.?, 17402.48.0.?, $\ldots$	$[(55377, 12983683), (30207/2, 4201643/2)]$	$1$
265776.ci1	265776ci2	265776.ci	265776ci	$2$	$7$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 113 \)	\( - 2^{14} \cdot 3 \cdot 7^{6} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$9492$	$96$	$2$	$9.749892840$	$1$		$0$	$32006016$	$3.310551$	$-39934705050538129/2823126576537804$	$1.05538$	$5.04649$	$1$	$[0, 1, 0, -5582880, -56348464908]$	\(y^2=x^3+x^2-5582880x-56348464908\)	7.24.0.a.2, 28.48.0-7.a.2.2, 678.2.0.?, 4746.48.2.?, 9492.96.2.?	$[(73018/3, 17755424/3)]$	$1$
343746.v1	343746v2	343746.v	343746v	$2$	$7$	\( 2 \cdot 3^{2} \cdot 13^{2} \cdot 113 \)	\( - 2^{2} \cdot 3^{7} \cdot 13^{6} \cdot 113^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$61698$	$96$	$2$	$18.71130113$	$1$		$0$	$49787136$	$3.476227$	$-39934705050538129/2823126576537804$	$1.05538$	$5.10061$	$1$	$[1, -1, 1, -10831073, 152263285373]$	\(y^2+xy+y=x^3-x^2-10831073x+152263285373\)	7.24.0.a.2, 273.48.0.?, 678.2.0.?, 4746.48.2.?, 20566.48.0.?, $\ldots$	$[(-452771061/275, 1097428814462/275)]$	$1$
358662.y1	358662y2	358662.y	358662y	$2$	$7$	\( 2 \cdot 3 \cdot 23^{2} \cdot 113 \)	\( - 2^{2} \cdot 3 \cdot 23^{6} \cdot 113^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$109158$	$96$	$2$	$1$	$49$	$7$	$0$	$44008272$	$3.212193$	$-39934705050538129/2823126576537804$	$1.05538$	$4.83595$	$1$	$[1, 0, 0, -3767020, 31230058268]$	\(y^2+xy=x^3-3767020x+31230058268\)	7.24.0.a.2, 161.48.0.?, 678.2.0.?, 4746.48.2.?, 109158.96.2.?	$[ ]$	$1$
406800.dc1	406800dc2	406800.dc	406800dc	$2$	$7$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 113 \)	\( - 2^{14} \cdot 3^{7} \cdot 5^{6} \cdot 113^{7} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$47460$	$96$	$2$	$5.102436625$	$1$		$4$	$94832640$	$3.691620$	$-39934705050538129/2823126576537804$	$1.05538$	$5.23422$	$1$	$[0, 0, 0, -25635675, -554430869750]$	\(y^2=x^3-25635675x-554430869750\)	7.24.0.a.2, 420.48.0.?, 678.2.0.?, 4746.48.2.?, 15820.48.0.?, $\ldots$	$[(128781, 46172704), (11261, 764784)]$	$1$

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