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

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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
966.j3	966i2	966.j	966i	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$1920$	$1.030415$	$154502321244119857/55101928644$	$[1, 0, 0, -11179, -455731]$	\(y^2+xy=x^3-11179x-455731\)
2898.f3	2898e2	2898.f	2898e	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$15360$	$1.579721$	$154502321244119857/55101928644$	$[1, -1, 0, -100611, 12304737]$	\(y^2+xy=x^3-x^2-100611x+12304737\)
6762.bc3	6762bb2	6762.bc	6762bb	$4$	$4$	\( 2 \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$4$	$2$	$2$	$92160$	$2.003368$	$154502321244119857/55101928644$	$[1, 1, 1, -547772, 155767961]$	\(y^2+xy+y=x^3+x^2-547772x+155767961\)
7728.b3	7728l2	7728.b	7728l	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{14} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2.808790284$	$1$		$9$	$46080$	$1.723562$	$154502321244119857/55101928644$	$[0, -1, 0, -178864, 29166784]$	\(y^2=x^3-x^2-178864x+29166784\)
20286.g3	20286x2	20286.g	20286x	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{18} \cdot 7^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$6.809590022$	$1$		$4$	$737280$	$2.552677$	$154502321244119857/55101928644$	$[1, -1, 0, -4929948, -4210664900]$	\(y^2+xy=x^3-x^2-4929948x-4210664900\)
22218.bh3	22218bh2	22218.bh	22218bh	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 23^{2} \)	\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 23^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$3.975705958$	$1$		$4$	$1013760$	$2.598160$	$154502321244119857/55101928644$	$[1, 0, 0, -5913702, 5533051680]$	\(y^2+xy=x^3-5913702x+5533051680\)
23184.bt3	23184bz2	23184.bt	23184bz	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{14} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$12.76816186$	$1$		$3$	$368640$	$2.272869$	$154502321244119857/55101928644$	$[0, 0, 0, -1609779, -785893390]$	\(y^2=x^3-1609779x-785893390\)
24150.s3	24150j2	24150.s	24150j	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$245760$	$1.835133$	$154502321244119857/55101928644$	$[1, 1, 0, -279475, -56966375]$	\(y^2+xy=x^3+x^2-279475x-56966375\)
30912.v3	30912e2	30912.v	30912e	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{20} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$4$	$2$	$3$	$368640$	$2.070137$	$154502321244119857/55101928644$	$[0, -1, 0, -715457, -232618815]$	\(y^2=x^3-x^2-715457x-232618815\)
30912.ch3	30912ch2	30912.ch	30912ch	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \)	\( 2^{20} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$368640$	$2.070137$	$154502321244119857/55101928644$	$[0, 1, 0, -715457, 232618815]$	\(y^2=x^3+x^2-715457x+232618815\)
54096.cz3	54096cs2	54096.cz	54096cs	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{14} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$3$	$2211840$	$2.696518$	$154502321244119857/55101928644$	$[0, 1, 0, -8764352, -9986678220]$	\(y^2=x^3+x^2-8764352x-9986678220\)
66654.l3	66654v2	66654.l	66654v	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 23^{2} \)	\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 23^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$9$	$3$	$2$	$8110080$	$3.147469$	$154502321244119857/55101928644$	$[1, -1, 0, -53223318, -149392395360]$	\(y^2+xy=x^3-x^2-53223318x-149392395360\)
72450.ea3	72450eq2	72450.ea	72450eq	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{2} \cdot 3^{18} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4.476943147$	$1$		$4$	$1966080$	$2.384441$	$154502321244119857/55101928644$	$[1, -1, 1, -2515280, 1535576847]$	\(y^2+xy+y=x^3-x^2-2515280x+1535576847\)
92736.bg3	92736bh2	92736.bg	92736bh	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{20} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$2949120$	$2.619442$	$154502321244119857/55101928644$	$[0, 0, 0, -6439116, 6287147120]$	\(y^2=x^3-6439116x+6287147120\)
92736.bj3	92736fq2	92736.bj	92736fq	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \)	\( 2^{20} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10.40376757$	$1$		$3$	$2949120$	$2.619442$	$154502321244119857/55101928644$	$[0, 0, 0, -6439116, -6287147120]$	\(y^2=x^3-6439116x-6287147120\)
116886.p3	116886w2	116886.p	116886w	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 11^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 11^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$0.592369540$	$1$		$16$	$2457600$	$2.229362$	$154502321244119857/55101928644$	$[1, 0, 1, -1352662, 605225300]$	\(y^2+xy+y=x^3-1352662x+605225300\)
155526.bu3	155526bf2	155526.bu	155526bf	$4$	$4$	\( 2 \cdot 3 \cdot 7^{2} \cdot 23^{2} \)	\( 2^{2} \cdot 3^{12} \cdot 7^{8} \cdot 23^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.2	2Cs	$1$	$4$	$2$	$2$	$48660480$	$3.571117$	$154502321244119857/55101928644$	$[1, 1, 1, -289771399, -1898126497639]$	\(y^2+xy+y=x^3+x^2-289771399x-1898126497639\)
162288.cf3	162288v2	162288.cf	162288v	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{14} \cdot 3^{18} \cdot 7^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$7.263804512$	$1$		$5$	$17694720$	$3.245823$	$154502321244119857/55101928644$	$[0, 0, 0, -78879171, 269561432770]$	\(y^2=x^3-78879171x+269561432770\)
163254.bs3	163254ck2	163254.bs	163254ck	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 13^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$4423680$	$2.312889$	$154502321244119857/55101928644$	$[1, 0, 1, -1889255, -999351754]$	\(y^2+xy+y=x^3-1889255x-999351754\)
169050.eg3	169050gv2	169050.eg	169050gv	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 5^{6} \cdot 7^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$0.875871458$	$1$		$14$	$11796480$	$2.808090$	$154502321244119857/55101928644$	$[1, 0, 1, -13694301, 19498383748]$	\(y^2+xy+y=x^3-13694301x+19498383748\)
177744.bj3	177744cb2	177744.bj	177744cb	$4$	$4$	\( 2^{4} \cdot 3 \cdot 7 \cdot 23^{2} \)	\( 2^{14} \cdot 3^{12} \cdot 7^{2} \cdot 23^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$37.90491814$	$1$		$3$	$24330240$	$3.291309$	$154502321244119857/55101928644$	$[0, -1, 0, -94619232, -354115307520]$	\(y^2=x^3-x^2-94619232x-354115307520\)
193200.dv3	193200bz2	193200.dv	193200bz	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{14} \cdot 3^{12} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1.267465408$	$1$		$41$	$5898240$	$2.528282$	$154502321244119857/55101928644$	$[0, 1, 0, -4471608, 3636904788]$	\(y^2=x^3+x^2-4471608x+3636904788\)
216384.be3	216384cu2	216384.be	216384cu	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{20} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$20.78697468$	$1$		$3$	$17694720$	$3.043091$	$154502321244119857/55101928644$	$[0, -1, 0, -35057409, -79858368351]$	\(y^2=x^3-x^2-35057409x-79858368351\)
216384.fj3	216384ez2	216384.fj	216384ez	$4$	$4$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \)	\( 2^{20} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$4.052956367$	$1$		$25$	$17694720$	$3.043091$	$154502321244119857/55101928644$	$[0, 1, 0, -35057409, 79858368351]$	\(y^2=x^3+x^2-35057409x+79858368351\)
279174.cc3	279174cc2	279174.cc	279174cc	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 17^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 17^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$27.85281143$	$1$		$2$	$8847360$	$2.447021$	$154502321244119857/55101928644$	$[1, 1, 1, -3230737, -2235775669]$	\(y^2+xy+y=x^3+x^2-3230737x-2235775669\)
348726.b3	348726b2	348726.b	348726b	$4$	$4$	\( 2 \cdot 3 \cdot 7 \cdot 19^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 19^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3.725089341$	$1$		$4$	$13824000$	$2.502632$	$154502321244119857/55101928644$	$[1, 1, 0, -4035626, 3117787680]$	\(y^2+xy=x^3+x^2-4035626x+3117787680\)
350658.ed3	350658ed2	350658.ed	350658ed	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 11^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 11^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$27.35410563$	$1$		$2$	$19660800$	$2.778667$	$154502321244119857/55101928644$	$[1, -1, 1, -12173954, -16341083107]$	\(y^2+xy+y=x^3-x^2-12173954x-16341083107\)
466578.cj3	466578cj2	466578.cj	466578cj	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23^{2} \)	\( 2^{2} \cdot 3^{18} \cdot 7^{8} \cdot 23^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$389283840$	$4.120422$	$154502321244119857/55101928644$	$[1, -1, 0, -2607942591, 51246807493657]$	\(y^2+xy=x^3-x^2-2607942591x+51246807493657\)
489762.dv3	489762dv2	489762.dv	489762dv	$4$	$4$	\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \cdot 23 \)	\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 13^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$35389440$	$2.862194$	$154502321244119857/55101928644$	$[1, -1, 1, -17003291, 26982497351]$	\(y^2+xy+y=x^3-x^2-17003291x+26982497351\)