Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

Sort order

Select

Results (29 matches)

 

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
2280.b3	2280a2	2280.b	2280a	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$768$	$0.238370$	$445138564/81225$	$[0, -1, 0, -160, 700]$	\(y^2=x^3-x^2-160x+700\)
4560.ba3	4560j2	4560.ba	4560j	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$1536$	$0.238370$	$445138564/81225$	$[0, 1, 0, -160, -700]$	\(y^2=x^3+x^2-160x-700\)
6840.e3	6840m2	6840.e	6840m	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$2.340389439$	$1$		$7$	$6144$	$0.787676$	$445138564/81225$	$[0, 0, 0, -1443, -17458]$	\(y^2=x^3-1443x-17458\)
11400.bh3	11400bh2	11400.bh	11400bh	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3.461579915$	$1$		$5$	$18432$	$1.043089$	$445138564/81225$	$[0, 1, 0, -4008, 79488]$	\(y^2=x^3+x^2-4008x+79488\)
13680.q3	13680l2	13680.q	13680l	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1.110292403$	$1$		$13$	$12288$	$0.787676$	$445138564/81225$	$[0, 0, 0, -1443, 17458]$	\(y^2=x^3-1443x+17458\)
18240.m3	18240bs2	18240.m	18240bs	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$12288$	$0.584944$	$445138564/81225$	$[0, -1, 0, -641, -4959]$	\(y^2=x^3-x^2-641x-4959\)
18240.bu3	18240bh2	18240.bu	18240bh	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19 \)	\( 2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2.112262695$	$1$		$7$	$12288$	$0.584944$	$445138564/81225$	$[0, 1, 0, -641, 4959]$	\(y^2=x^3+x^2-641x+4959\)
22800.s3	22800h2	22800.s	22800h	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2.718141474$	$1$		$25$	$36864$	$1.043089$	$445138564/81225$	$[0, -1, 0, -4008, -79488]$	\(y^2=x^3-x^2-4008x-79488\)
34200.bk3	34200q2	34200.bk	34200q	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$147456$	$1.592396$	$445138564/81225$	$[0, 0, 0, -36075, -2182250]$	\(y^2=x^3-36075x-2182250\)
43320.bd3	43320bg2	43320.bd	43320bg	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$13.90978915$	$1$		$3$	$276480$	$1.710588$	$445138564/81225$	$[0, 1, 0, -57880, -4454272]$	\(y^2=x^3+x^2-57880x-4454272\)
54720.dn3	54720ei2	54720.dn	54720ei	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{2} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3.397025860$	$1$		$21$	$98304$	$1.134249$	$445138564/81225$	$[0, 0, 0, -5772, 139664]$	\(y^2=x^3-5772x+139664\)
54720.ea3	54720cc2	54720.ea	54720cc	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$3$	$98304$	$1.134249$	$445138564/81225$	$[0, 0, 0, -5772, -139664]$	\(y^2=x^3-5772x-139664\)
68400.dt3	68400bw2	68400.dt	68400bw	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{8} \cdot 5^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.986393885$	$1$		$9$	$294912$	$1.592396$	$445138564/81225$	$[0, 0, 0, -36075, 2182250]$	\(y^2=x^3-36075x+2182250\)
86640.bj3	86640j2	86640.bj	86640j	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$3.442701726$	$1$		$7$	$552960$	$1.710588$	$445138564/81225$	$[0, -1, 0, -57880, 4454272]$	\(y^2=x^3-x^2-57880x+4454272\)
91200.ce3	91200y2	91200.ce	91200y	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$294912$	$1.389662$	$445138564/81225$	$[0, -1, 0, -16033, 651937]$	\(y^2=x^3-x^2-16033x+651937\)
91200.hh3	91200hl2	91200.hh	91200hl	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{2} \cdot 5^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$5.308695007$	$1$		$5$	$294912$	$1.389662$	$445138564/81225$	$[0, 1, 0, -16033, -651937]$	\(y^2=x^3+x^2-16033x-651937\)
111720.bn3	111720w2	111720.bn	111720w	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$294912$	$1.211325$	$445138564/81225$	$[0, 1, 0, -7856, -224400]$	\(y^2=x^3+x^2-7856x-224400\)
129960.s3	129960r2	129960.s	129960r	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4.316154136$	$1$		$7$	$2211840$	$2.259895$	$445138564/81225$	$[0, 0, 0, -520923, 119744422]$	\(y^2=x^3-520923x+119744422\)
216600.bf3	216600ee2	216600.bf	216600ee	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 19^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$4$	$2$	$3$	$6635520$	$2.515308$	$445138564/81225$	$[0, -1, 0, -1447008, -553889988]$	\(y^2=x^3-x^2-1447008x-553889988\)
223440.j3	223440hg2	223440.j	223440hg	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.814651525$	$1$		$31$	$589824$	$1.211325$	$445138564/81225$	$[0, -1, 0, -7856, 224400]$	\(y^2=x^3-x^2-7856x+224400\)
259920.bz3	259920bz2	259920.bz	259920bz	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3.967017602$	$1$		$7$	$4423680$	$2.259895$	$445138564/81225$	$[0, 0, 0, -520923, -119744422]$	\(y^2=x^3-520923x-119744422\)
273600.hk3	273600hk2	273600.hk	273600hk	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$2.809575645$	$1$		$9$	$2359296$	$1.938969$	$445138564/81225$	$[0, 0, 0, -144300, 17458000]$	\(y^2=x^3-144300x+17458000\)
273600.ji3	273600ji2	273600.ji	273600ji	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4.680037965$	$1$		$7$	$2359296$	$1.938969$	$445138564/81225$	$[0, 0, 0, -144300, -17458000]$	\(y^2=x^3-144300x-17458000\)
275880.u3	275880u2	275880.u	275880u	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 11^{6} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3.837157963$	$1$		$5$	$983040$	$1.437317$	$445138564/81225$	$[0, -1, 0, -19400, -854148]$	\(y^2=x^3-x^2-19400x-854148\)
335160.bz3	335160bz2	335160.bz	335160bz	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 7^{6} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$2359296$	$1.760632$	$445138564/81225$	$[0, 0, 0, -70707, 5988094]$	\(y^2=x^3-70707x+5988094\)
346560.bf3	346560bf2	346560.bf	346560bf	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$4423680$	$2.057163$	$445138564/81225$	$[0, -1, 0, -231521, -35402655]$	\(y^2=x^3-x^2-231521x-35402655\)
346560.hh3	346560hh2	346560.hh	346560hh	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$4$	$2$	$3$	$4423680$	$2.057163$	$445138564/81225$	$[0, 1, 0, -231521, 35402655]$	\(y^2=x^3+x^2-231521x+35402655\)
385320.i3	385320i2	385320.i	385320i	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 13^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 13^{6} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.938954414$	$1$		$9$	$1769472$	$1.520845$	$445138564/81225$	$[0, -1, 0, -27096, 1429596]$	\(y^2=x^3-x^2-27096x+1429596\)
433200.ic3	433200ic2	433200.ic	433200ic	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 19^{2} \)	\( 2^{10} \cdot 3^{2} \cdot 5^{8} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$5.953811000$	$1$		$5$	$13271040$	$2.515308$	$445138564/81225$	$[0, 1, 0, -1447008, 553889988]$	\(y^2=x^3+x^2-1447008x+553889988\)