Elliptic curves over $\Q$ of conductor 69366

Results (25 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	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
69366.a1	69366c1	69366.a	69366c	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{5} \cdot 3^{4} \cdot 11^{3} \cdot 1051 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$0.792414393$	$1$		$12$	$44160$	$0.534435$	$9845751989737/3625899552$	$0.84103$	$2.68392$	$[1, 1, 0, -446, 2004]$	\(y^2+xy=x^3+x^2-446x+2004\)	92488.2.0.?	$[(-1, 50), (-23, 39)]$
69366.b1	69366e1	69366.b	69366e	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{7} \cdot 3^{21} \cdot 11 \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$23.69209960$	$1$		$0$	$486864$	$1.824621$	$-62605248418149730489/15479314352625024$	$0.93162$	$4.12115$	$[1, 1, 0, -82723, -10975091]$	\(y^2+xy=x^3+x^2-82723x-10975091\)	277464.2.0.?	$[(15451019133/4823, 1655634301289116/4823)]$
69366.c1	69366f1	69366.c	69366f	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2 \cdot 3^{3} \cdot 11 \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$1.246619437$	$1$		$2$	$16416$	$-0.060703$	$-76711450249/624294$	$0.78268$	$2.24966$	$[1, 1, 0, -88, 286]$	\(y^2+xy=x^3+x^2-88x+286\)	277464.2.0.?	$[(5, -1)]$
69366.d1	69366d1	69366.d	69366d	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{3} \cdot 3^{4} \cdot 11^{7} \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$0.370520086$	$1$		$4$	$338688$	$1.675331$	$1278371889198317049625/13271698835208$	$0.94100$	$4.35985$	$[1, 1, 0, -226105, 41287741]$	\(y^2+xy=x^3+x^2-226105x+41287741\)	92488.2.0.?	$[(297, 517)]$
69366.e1	69366a1	69366.e	69366a	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{17} \cdot 3 \cdot 11^{3} \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$15.23403224$	$1$		$0$	$119136$	$1.043526$	$-26198337627891001/550062391296$	$0.88684$	$3.39460$	$[1, 1, 0, -6187, -193283]$	\(y^2+xy=x^3+x^2-6187x-193283\)	277464.2.0.?	$[(4080949/33, 8176279631/33)]$
69366.f1	69366b1	69366.f	69366b	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{3} \cdot 3^{5} \cdot 11^{5} \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$6.229905547$	$1$		$0$	$170400$	$0.889581$	$-3849961626217/329050384344$	$0.89903$	$3.04840$	$[1, 1, 0, -326, -27828]$	\(y^2+xy=x^3+x^2-326x-27828\)	277464.2.0.?	$[(307/3, 805/3)]$
69366.g1	69366k1	69366.g	69366k	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{3} \cdot 3^{10} \cdot 11 \cdot 1051 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$0.877140928$	$1$		$12$	$82560$	$0.611861$	$68523370149961/5461323912$	$0.84681$	$2.85797$	$[1, 0, 1, -853, -8968]$	\(y^2+xy+y=x^3-853x-8968\)	92488.2.0.?	$[(-20, 23), (34, 23)]$
69366.h1	69366g1	69366.h	69366g	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{3} \cdot 3 \cdot 11 \cdot 1051 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$1$	$1$		$0$	$12168$	$-0.246550$	$-702595369/277464$	$0.73603$	$1.87407$	$[1, 0, 1, -19, 38]$	\(y^2+xy+y=x^3-19x+38\)	277464.2.0.?	$[]$
69366.i1	69366i1	69366.i	69366i	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{14} \cdot 3 \cdot 11^{2} \cdot 1051 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$25224$	$12$	$0$	$11.84961213$	$1$		$1$	$90048$	$0.906905$	$54640564143369625/6250708992$	$0.89081$	$3.45735$	$[1, 0, 1, -7906, -271180]$	\(y^2+xy+y=x^3-7906x-271180\)	2.3.0.a.1, 8.6.0.d.1, 6306.6.0.?, 25224.12.0.?	$[(382161/40, 209181739/40)]$
69366.i2	69366i2	69366.i	69366i	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{7} \cdot 3^{2} \cdot 11^{4} \cdot 1051^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$25224$	$12$	$0$	$5.924806067$	$1$		$0$	$180096$	$1.253479$	$-42415439299593625/18630677653632$	$0.89653$	$3.48529$	$[1, 0, 1, -7266, -316748]$	\(y^2+xy+y=x^3-7266x-316748\)	2.3.0.a.1, 8.6.0.a.1, 12612.6.0.?, 25224.12.0.?	$[(3707/2, 221019/2)]$
69366.j1	69366h1	69366.j	69366h	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{3} \cdot 3^{4} \cdot 11^{5} \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$2.378886773$	$1$		$2$	$71040$	$0.863174$	$1434371386041433/109683461448$	$0.86903$	$3.13080$	$[1, 0, 1, -2350, -41032]$	\(y^2+xy+y=x^3-2350x-41032\)	92488.2.0.?	$[(-32, 56)]$
69366.k1	69366j1	69366.k	69366j	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{9} \cdot 3^{7} \cdot 11 \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$1.108910617$	$1$		$4$	$267120$	$1.313967$	$-50197387024796594617/12945360384$	$0.92673$	$4.06942$	$[1, 0, 1, -76852, 8193842]$	\(y^2+xy+y=x^3-76852x+8193842\)	277464.2.0.?	$[(160, -79)]$
69366.l1	69366r1	69366.l	69366r	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{9} \cdot 3^{4} \cdot 11 \cdot 1051 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$0.462914060$	$1$		$16$	$52992$	$0.380664$	$2300490759601/479457792$	$0.82162$	$2.55349$	$[1, 1, 1, -275, -1519]$	\(y^2+xy+y=x^3+x^2-275x-1519\)	92488.2.0.?	$[(-9, 22), (27, 94)]$
69366.m1	69366o1	69366.m	69366o	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{7} \cdot 3^{3} \cdot 11 \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$5.328931626$	$1$		$2$	$100800$	$1.007002$	$-2593675442589394177/39954816$	$0.91221$	$3.80363$	$[1, 1, 1, -28624, -1875919]$	\(y^2+xy+y=x^3+x^2-28624x-1875919\)	277464.2.0.?	$[(457, 8757)]$
69366.n1	69366n1	69366.n	69366n	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2 \cdot 3^{12} \cdot 11 \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$2.821143123$	$1$		$0$	$49536$	$0.676153$	$138935491574257/12287978802$	$0.94914$	$2.92138$	$[1, 1, 1, -1079, 12107]$	\(y^2+xy+y=x^3+x^2-1079x+12107\)	92488.2.0.?	$[(435/2, 8309/2)]$
69366.o1	69366p1	69366.o	69366p	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{11} \cdot 3 \cdot 11^{3} \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$0.207006715$	$1$		$6$	$38544$	$0.640714$	$-69370801987969/8594724864$	$0.84820$	$2.87647$	$[1, 1, 1, -856, 10265]$	\(y^2+xy+y=x^3+x^2-856x+10265\)	277464.2.0.?	$[(37, 157)]$
69366.p1	69366m1	69366.p	69366m	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{5} \cdot 3^{7} \cdot 11^{3} \cdot 1051 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$1$	$1$		$0$	$74760$	$0.796559$	$115295088815711/97899287904$	$0.86789$	$2.90464$	$[1, 1, 1, 1014, -8073]$	\(y^2+xy+y=x^3+x^2+1014x-8073\)	277464.2.0.?	$[]$
69366.q1	69366l1	69366.q	69366l	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{7} \cdot 3^{4} \cdot 11 \cdot 1051 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$0.439882141$	$1$		$16$	$44800$	$0.442893$	$67443993402625/119864448$	$0.84505$	$2.85654$	$[1, 1, 1, -848, 9137]$	\(y^2+xy+y=x^3+x^2-848x+9137\)	92488.2.0.?	$[(15, 1), (-3, 109)]$
69366.r1	69366q1	69366.r	69366q	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{39} \cdot 3^{4} \cdot 11 \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$0.632871614$	$1$		$6$	$828672$	$2.110710$	$2226300559224995953153/514813884113092608$	$0.94794$	$4.40961$	$[1, 1, 1, -272032, -42429247]$	\(y^2+xy+y=x^3+x^2-272032x-42429247\)	92488.2.0.?	$[(661, 7861)]$
69366.s1	69366v1	69366.s	69366v	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2^{15} \cdot 3^{6} \cdot 11^{3} \cdot 1051 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$0.088805985$	$1$		$34$	$328320$	$1.326670$	$286494848761002337/33416290271232$	$0.90265$	$3.60599$	$[1, 0, 0, -13734, 552420]$	\(y^2+xy=x^3-13734x+552420\)	92488.2.0.?	$[(-84, 1098), (48, 42)]$
69366.t1	69366t1	69366.t	69366t	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{3} \cdot 3^{3} \cdot 11^{3} \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$2.194289222$	$1$		$2$	$27648$	$0.355669$	$-1921886786737/302158296$	$0.81879$	$2.55892$	$[1, 0, 0, -259, -1831]$	\(y^2+xy=x^3-259x-1831\)	277464.2.0.?	$[(20, 23)]$
69366.u1	69366w2	69366.u	69366w	$2$	$7$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{3} \cdot 3 \cdot 11 \cdot 1051^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$1942248$	$96$	$2$	$30.93937299$	$1$		$0$	$13253520$	$3.486423$	$-925492188434597796818942768449/373958095272087819200664$	$1.00515$	$6.19000$	$[1, 0, 0, -203025076, -1113860484568]$	\(y^2+xy=x^3-203025076x-1113860484568\)	7.48.0-7.a.2.2, 277464.2.0.?, 1942248.96.2.?	$[(24880589116471/17290, 121936578964908273649/17290)]$
69366.u2	69366w1	69366.u	69366w	$2$	$7$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{21} \cdot 3^{7} \cdot 11^{7} \cdot 1051 \)	$1$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$1942248$	$96$	$2$	$4.419910427$	$1$		$10$	$1893360$	$2.513470$	$8822561460536124355391/93935597925332680704$	$0.97730$	$4.78938$	$[1, 0, 0, 430484, 453494672]$	\(y^2+xy=x^3+430484x+453494672\)	7.48.0-7.a.1.2, 277464.2.0.?, 1942248.96.2.?	$[(176, 23036)]$
69366.v1	69366s1	69366.v	69366s	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( - 2^{5} \cdot 3^{5} \cdot 11 \cdot 1051 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$277464$	$2$	$0$	$0.315250148$	$1$		$6$	$33200$	$0.212666$	$80565593759/89898336$	$0.80435$	$2.25280$	$[1, 0, 0, 90, 324]$	\(y^2+xy=x^3+90x+324\)	277464.2.0.?	$[(0, 18)]$
69366.w1	69366u1	69366.w	69366u	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 1051 \)	\( 2 \cdot 3^{2} \cdot 11 \cdot 1051^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$92488$	$2$	$0$	$1$	$4$	$2$	$0$	$100224$	$0.963088$	$9147293661734353/229865258898$	$0.88025$	$3.29701$	$[1, 0, 0, -4357, 107903]$	\(y^2+xy=x^3-4357x+107903\)	92488.2.0.?	$[]$