Elliptic curve search results

Results (18 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	Manin constant
3315.f2	3315c3	3315.f	3315c	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{12} \cdot 5^{4} \cdot 13^{3} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$312$	$48$	$0$	$1.687267765$	$1$		$0$	$239616$	$2.911583$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$7.34160$	$[1, 1, 0, -8591808, -9068791113]$	\(y^2+xy=x^3+x^2-8591808x-9068791113\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 26.6.0.b.1, 52.24.0-52.g.1.1, $\ldots$	$[(41439/2, 8014011/2)]$	$1$
9945.b2	9945j4	9945.b	9945j	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{18} \cdot 5^{4} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$312$	$48$	$0$	$1$	$1$		$0$	$1916928$	$3.460892$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$7.18148$	$[1, -1, 1, -77326277, 244780033776]$	\(y^2+xy+y=x^3-x^2-77326277x+244780033776\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$	$[ ]$	$1$
16575.b2	16575g3	16575.b	16575g	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{12} \cdot 5^{10} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$0$	$5750784$	$3.716305$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$7.11936$	$[1, 0, 0, -214795213, -1133169298708]$	\(y^2+xy=x^3-214795213x-1133169298708\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.ba.1, 26.6.0.b.1, $\ldots$	$[ ]$	$1$
43095.c2	43095h3	43095.c	43095h	$4$	$4$	\( 3 \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 3^{12} \cdot 5^{4} \cdot 13^{9} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$312$	$48$	$0$	$1.915758674$	$1$		$2$	$40255488$	$4.194061$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$7.01913$	$[1, 1, 1, -1452015640, -19916873997220]$	\(y^2+xy+y=x^3+x^2-1452015640x-19916873997220\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.1, 26.6.0.b.1, 52.24.0-52.g.1.1, $\ldots$	$[(-19742, 1036968)]$	$1$
49725.u2	49725h3	49725.u	49725h	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{18} \cdot 5^{10} \cdot 13^{3} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$10.16777716$	$1$		$0$	$46006272$	$4.265610$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$7.00564$	$[1, -1, 0, -1933156917, 30595571065116]$	\(y^2+xy=x^3-x^2-1933156917x+30595571065116\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 40.12.0-4.c.1.5, $\ldots$	$[(812904/11, 5628568278/11)]$	$1$
53040.bo2	53040cp3	53040.bo	53040cp	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{12} \cdot 5^{4} \cdot 13^{3} \cdot 17^{8} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$312$	$48$	$0$	$0.664153961$	$1$		$17$	$15335424$	$3.604733$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.23509$	$[0, 1, 0, -137468936, 580127693364]$	\(y^2=x^3+x^2-137468936x+580127693364\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 26.6.0.b.1, 52.24.0-52.g.1.2, $\ldots$	$[(8284, 99450)]$	$1$
56355.s2	56355v3	56355.s	56355v	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 3^{12} \cdot 5^{4} \cdot 13^{3} \cdot 17^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5304$	$48$	$0$	$1$	$1$		$0$	$69009408$	$4.328194$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.99414$	$[1, 0, 1, -2483032663, -44537589509887]$	\(y^2+xy+y=x^3-2483032663x-44537589509887\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 52.12.0.g.1, $\ldots$	$[ ]$	$1$
129285.bc2	129285r3	129285.bc	129285r	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 3^{18} \cdot 5^{4} \cdot 13^{9} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.14	2B	$312$	$48$	$0$	$1$	$1$		$0$	$322043904$	$4.743362$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.92400$	$[1, -1, 0, -13068140760, 537742529784175]$	\(y^2+xy=x^3-x^2-13068140760x+537742529784175\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.5, $\ldots$	$[ ]$	$1$
159120.cl2	159120b4	159120.cl	159120b	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{18} \cdot 5^{4} \cdot 13^{3} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$312$	$48$	$0$	$2.002562366$	$1$		$7$	$122683392$	$4.154037$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.21353$	$[0, 0, 0, -1237220427, -15664684941254]$	\(y^2=x^3-1237220427x-15664684941254\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[(-17833, 852930)]$	$1$
162435.ce2	162435bx3	162435.ce	162435bx	$4$	$4$	\( 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{12} \cdot 5^{4} \cdot 7^{6} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2184$	$48$	$0$	$1$	$1$		$0$	$69009408$	$3.884541$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$5.93331$	$[1, 0, 1, -420998618, 3109332355931]$	\(y^2+xy+y=x^3-420998618x+3109332355931\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 28.12.0-4.c.1.1, $\ldots$	$[ ]$	$1$
169065.j2	169065j3	169065.j	169065j	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 3^{18} \cdot 5^{4} \cdot 13^{3} \cdot 17^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5304$	$48$	$0$	$6.320466154$	$1$		$0$	$552075264$	$4.877495$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.90341$	$[1, -1, 1, -22347293963, 1202514916766942]$	\(y^2+xy+y=x^3-x^2-22347293963x+1202514916766942\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 52.12.0.g.1, $\ldots$	$[(-763536/5, 5387863202/5)]$	$1$
212160.bx2	212160ca3	212160.bx	212160ca	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{12} \cdot 5^{4} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$312$	$48$	$0$	$1$	$1$		$1$	$122683392$	$3.951305$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$5.86944$	$[0, -1, 0, -549875745, 4641571422657]$	\(y^2=x^3-x^2-549875745x+4641571422657\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 24.24.0-24.ba.1.14, 26.6.0.b.1, $\ldots$	$[ ]$	$1$
212160.hu2	212160fc4	212160.hu	212160fc	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{12} \cdot 5^{4} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$312$	$48$	$0$	$1$	$1$		$1$	$122683392$	$3.951305$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$5.86944$	$[0, 1, 0, -549875745, -4641571422657]$	\(y^2=x^3+x^2-549875745x-4641571422657\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 24.24.0-24.ba.1.6, 26.6.0.b.1, $\ldots$	$[ ]$	$1$
215475.bt2	215475bp4	215475.bt	215475bp	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{12} \cdot 5^{10} \cdot 13^{9} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$25$	$5$	$0$	$966131712$	$4.998779$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.88557$	$[1, 0, 1, -36300391001, -2489536648870477]$	\(y^2+xy+y=x^3-36300391001x-2489536648870477\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.ba.1, 26.6.0.b.1, $\ldots$	$[ ]$	$1$
265200.dr2	265200dr3	265200.dr	265200dr	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{12} \cdot 5^{10} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$16$	$2$	$1$	$368050176$	$4.409447$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.20479$	$[0, -1, 0, -3436723408, 72522835117312]$	\(y^2=x^3-x^2-3436723408x+72522835117312\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.ba.1, 26.6.0.b.1, $\ldots$	$[ ]$	$1$
281775.p2	281775p4	281775.p	281775p	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( 3^{12} \cdot 5^{10} \cdot 13^{3} \cdot 17^{14} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$26520$	$48$	$0$	$132.1025584$	$1$		$0$	$1656225792$	$5.132912$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$6.86664$	$[1, 1, 1, -62075816563, -5567198688735844]$	\(y^2+xy+y=x^3+x^2-62075816563x-5567198688735844\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 52.12.0.g.1, $\ldots$	$[(-48514158814986351623051770193593720961816833635702442153699/638492237419738261719348385, 3036907695147213202257933209010207417765269125264759710558852964839240837431797923712419/638492237419738261719348385)]$	$1$
401115.h2	401115h3	401115.h	401115h	$4$	$4$	\( 3 \cdot 5 \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 3^{12} \cdot 5^{4} \cdot 11^{6} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3432$	$48$	$0$	$1$	$1$		$0$	$306708480$	$4.110535$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$5.72779$	$[1, 1, 1, -1039608831, 12065362927344]$	\(y^2+xy+y=x^3+x^2-1039608831x+12065362927344\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 44.12.0-4.c.1.1, $\ldots$	$[ ]$	$1$
487305.w2	487305w4	487305.w	487305w	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{18} \cdot 5^{4} \cdot 7^{6} \cdot 13^{3} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2184$	$48$	$0$	$1$	$1$		$0$	$552075264$	$4.433846$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$5.93890$	$[1, -1, 1, -3788987558, -83951973610144]$	\(y^2+xy+y=x^3-x^2-3788987558x-83951973610144\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 26.6.0.b.1, 52.12.0.g.1, $\ldots$	$[ ]$	$1$

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