Elliptic curve search results

Results (24 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
2072.e1	2072c2	2072.e	2072c	$2$	$2$	\( 2^{3} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 7^{6} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$9.354022090$	$1$		$1$	$1728$	$0.691491$	$169556172914/4353013$	$0.88931$	$4.38448$	$[0, -1, 0, -1464, -20596]$	\(y^2=x^3-x^2-1464x-20596\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(10765/6, 1105417/6)]$
4144.a1	4144e2	4144.a	4144e	$2$	$2$	\( 2^{4} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 7^{6} \cdot 37 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$0.409342356$	$1$		$27$	$3456$	$0.691491$	$169556172914/4353013$	$0.88931$	$4.01962$	$[0, 1, 0, -1464, 20596]$	\(y^2=x^3+x^2-1464x+20596\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(26, 28), (18, 20)]$
14504.b1	14504f2	14504.b	14504f	$2$	$2$	\( 2^{3} \cdot 7^{2} \cdot 37 \)	\( 2^{11} \cdot 7^{12} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$82944$	$1.664446$	$169556172914/4353013$	$0.88931$	$4.71255$	$[0, 1, 0, -71752, 7207920]$	\(y^2=x^3+x^2-71752x+7207920\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
16576.d1	16576f2	16576.d	16576f	$2$	$2$	\( 2^{6} \cdot 7 \cdot 37 \)	\( 2^{17} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$27648$	$1.038065$	$169556172914/4353013$	$0.88931$	$3.87413$	$[0, 1, 0, -5857, -170625]$	\(y^2=x^3+x^2-5857x-170625\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
16576.t1	16576s2	16576.t	16576s	$2$	$2$	\( 2^{6} \cdot 7 \cdot 37 \)	\( 2^{17} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$27648$	$1.038065$	$169556172914/4353013$	$0.88931$	$3.87413$	$[0, -1, 0, -5857, 170625]$	\(y^2=x^3-x^2-5857x+170625\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
18648.u1	18648z2	18648.u	18648z	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 3^{6} \cdot 7^{6} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$6.985203514$	$1$		$1$	$41472$	$1.240797$	$169556172914/4353013$	$0.88931$	$4.07513$	$[0, 0, 0, -13179, 569270]$	\(y^2=x^3-13179x+569270\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(1073/2, 32335/2)]$
29008.n1	29008g2	29008.n	29008g	$2$	$2$	\( 2^{4} \cdot 7^{2} \cdot 37 \)	\( 2^{11} \cdot 7^{12} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$165888$	$1.664446$	$169556172914/4353013$	$0.88931$	$4.39466$	$[0, -1, 0, -71752, -7207920]$	\(y^2=x^3-x^2-71752x-7207920\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
37296.cc1	37296ba2	37296.cc	37296ba	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 3^{6} \cdot 7^{6} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$2.723329299$	$1$		$3$	$82944$	$1.240797$	$169556172914/4353013$	$0.88931$	$3.80679$	$[0, 0, 0, -13179, -569270]$	\(y^2=x^3-13179x-569270\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(138, 490)]$
51800.b1	51800s2	51800.b	51800s	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 5^{6} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$221184$	$1.496210$	$169556172914/4353013$	$0.88931$	$3.97394$	$[0, 1, 0, -36608, -2647712]$	\(y^2=x^3+x^2-36608x-2647712\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
76664.j1	76664i2	76664.j	76664i	$2$	$2$	\( 2^{3} \cdot 7 \cdot 37^{2} \)	\( 2^{11} \cdot 7^{6} \cdot 37^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$25$	$5$	$1$	$2363904$	$2.496948$	$169556172914/4353013$	$0.88931$	$4.90314$	$[0, -1, 0, -2004672, -1067303380]$	\(y^2=x^3-x^2-2004672x-1067303380\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
103600.bz1	103600i2	103600.bz	103600i	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 5^{6} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$442368$	$1.496210$	$169556172914/4353013$	$0.88931$	$3.73542$	$[0, -1, 0, -36608, 2647712]$	\(y^2=x^3-x^2-36608x+2647712\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
116032.g1	116032bu2	116032.g	116032bu	$2$	$2$	\( 2^{6} \cdot 7^{2} \cdot 37 \)	\( 2^{17} \cdot 7^{12} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$1327104$	$2.011021$	$169556172914/4353013$	$0.88931$	$4.22886$	$[0, 1, 0, -287009, -57950369]$	\(y^2=x^3+x^2-287009x-57950369\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
116032.bq1	116032p2	116032.bq	116032p	$2$	$2$	\( 2^{6} \cdot 7^{2} \cdot 37 \)	\( 2^{17} \cdot 7^{12} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$5.066938175$	$1$		$1$	$1327104$	$2.011021$	$169556172914/4353013$	$0.88931$	$4.22886$	$[0, -1, 0, -287009, 57950369]$	\(y^2=x^3-x^2-287009x+57950369\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(1021/2, 8967/2)]$
130536.o1	130536e2	130536.o	130536e	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 37 \)	\( 2^{11} \cdot 3^{6} \cdot 7^{12} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$1990656$	$2.213753$	$169556172914/4353013$	$0.88931$	$4.39311$	$[0, 0, 0, -645771, -195259610]$	\(y^2=x^3-645771x-195259610\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
149184.bs1	149184eg2	149184.bs	149184eg	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 \)	\( 2^{17} \cdot 3^{6} \cdot 7^{6} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$6.477892403$	$1$		$1$	$663552$	$1.587370$	$169556172914/4353013$	$0.88931$	$3.71291$	$[0, 0, 0, -52716, 4554160]$	\(y^2=x^3-52716x+4554160\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(1528/3, 19052/3)]$
149184.bv1	149184q2	149184.bv	149184q	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 \)	\( 2^{17} \cdot 3^{6} \cdot 7^{6} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$3.396892159$	$1$		$3$	$663552$	$1.587370$	$169556172914/4353013$	$0.88931$	$3.71291$	$[0, 0, 0, -52716, -4554160]$	\(y^2=x^3-52716x-4554160\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(668, 16072)]$
153328.e1	153328j2	153328.e	153328j	$2$	$2$	\( 2^{4} \cdot 7 \cdot 37^{2} \)	\( 2^{11} \cdot 7^{6} \cdot 37^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$4727808$	$2.496948$	$169556172914/4353013$	$0.88931$	$4.61851$	$[0, 1, 0, -2004672, 1067303380]$	\(y^2=x^3+x^2-2004672x+1067303380\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
250712.p1	250712p2	250712.p	250712p	$2$	$2$	\( 2^{3} \cdot 7 \cdot 11^{2} \cdot 37 \)	\( 2^{11} \cdot 7^{6} \cdot 11^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$2211840$	$1.890438$	$169556172914/4353013$	$0.88931$	$3.85040$	$[0, -1, 0, -177184, 28121964]$	\(y^2=x^3-x^2-177184x+28121964\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
261072.ci1	261072ci2	261072.ci	261072ci	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 37 \)	\( 2^{11} \cdot 3^{6} \cdot 7^{12} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$7.453627557$	$1$		$1$	$3981312$	$2.213753$	$169556172914/4353013$	$0.88931$	$4.14897$	$[0, 0, 0, -645771, 195259610]$	\(y^2=x^3-645771x+195259610\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[(2153/2, 15203/2)]$
350168.i1	350168i2	350168.i	350168i	$2$	$2$	\( 2^{3} \cdot 7 \cdot 13^{2} \cdot 37 \)	\( 2^{11} \cdot 7^{6} \cdot 13^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$3317760$	$1.973965$	$169556172914/4353013$	$0.88931$	$3.82815$	$[0, -1, 0, -247472, -46239220]$	\(y^2=x^3-x^2-247472x-46239220\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
362600.ct1	362600ct2	362600.ct	362600ct	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 37 \)	\( 2^{11} \cdot 5^{6} \cdot 7^{12} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$10616832$	$2.469166$	$169556172914/4353013$	$0.88931$	$4.28192$	$[0, -1, 0, -1793808, 904577612]$	\(y^2=x^3-x^2-1793808x+904577612\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
414400.s1	414400s2	414400.s	414400s	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{17} \cdot 5^{6} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$3538944$	$1.842783$	$169556172914/4353013$	$0.88931$	$3.65660$	$[0, 1, 0, -146433, 21035263]$	\(y^2=x^3+x^2-146433x+21035263\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
414400.fb1	414400fb2	414400.fb	414400fb	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{17} \cdot 5^{6} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$3538944$	$1.842783$	$169556172914/4353013$	$0.88931$	$3.65660$	$[0, -1, 0, -146433, -21035263]$	\(y^2=x^3-x^2-146433x-21035263\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$
466200.cr1	466200cr2	466200.cr	466200cr	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 37 \)	\( 2^{11} \cdot 3^{6} \cdot 5^{6} \cdot 7^{6} \cdot 37 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$5308416$	$2.045517$	$169556172914/4353013$	$0.88931$	$3.80999$	$[0, 0, 0, -329475, 71158750]$	\(y^2=x^3-329475x+71158750\)	2.3.0.a.1, 28.6.0.c.1, 296.6.0.?, 2072.12.0.?	$[ ]$

  Download displayed columns for results to