Elliptic curves over $\Q$ of conductor 453299

Results (32 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
453299.a1	453299a1	453299.a	453299a	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{6} \cdot 11 \cdot 29^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1.464415091$	$1$		$4$	$22256640$	$2.313843$	$-5601816576/9251$	$0.88114$	$4.17131$	$[0, 0, 1, -1524733, 725700792]$	\(y^2+y=x^3-1524733x+725700792\)	22.2.0.a.1	$[(203, 20604)]$
453299.b1	453299b1	453299.b	453299b	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{4} \cdot 11^{4} \cdot 29^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$58$	$2$	$0$	$2.850334940$	$1$		$0$	$15321600$	$2.395767$	$1581667741696/424589$	$0.89423$	$4.30556$	$[0, 1, 1, -2733530, -1740045828]$	\(y^2+y=x^3+x^2-2733530x-1740045828\)	58.2.0.a.1	$[(-47354/7, 50709/7)]$
453299.c1	453299c1	453299.c	453299c	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{3} \cdot 11^{3} \cdot 29^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$154$	$2$	$0$	$5.349991153$	$1$		$2$	$14448960$	$2.397118$	$24395739136/1331$	$0.87868$	$4.35292$	$[0, 1, 1, -3357552, 2366772468]$	\(y^2+y=x^3+x^2-3357552x+2366772468\)	154.2.0.?	$[(1047, 492)]$
453299.d1	453299d1	453299.d	453299d	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{9} \cdot 11^{3} \cdot 29^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$154$	$2$	$0$	$36.67248032$	$1$		$0$	$101142720$	$3.370075$	$24395739136/1331$	$0.87868$	$5.24936$	$[0, -1, 1, -164520064, -812131996726]$	\(y^2+y=x^3-x^2-164520064x-812131996726\)	154.2.0.?	$[(156400686881823394/55899, 61852600768982706445502078/55899)]$
453299.e1	453299e1	453299.e	453299e	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{10} \cdot 11^{4} \cdot 29^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$58$	$2$	$0$	$1$	$1$		$0$	$107251200$	$3.368725$	$1581667741696/424589$	$0.89423$	$5.20199$	$[0, -1, 1, -133942986, 596567832958]$	\(y^2+y=x^3-x^2-133942986x+596567832958\)	58.2.0.a.1	$[]$
453299.f1	453299f1	453299.f	453299f	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{7} \cdot 11^{2} \cdot 29^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$406$	$2$	$0$	$1.721913552$	$1$		$0$	$1763328$	$1.058090$	$110592/847$	$0.70944$	$2.75602$	$[0, 0, 1, 1421, -72116]$	\(y^2+y=x^3+1421x-72116\)	406.2.0.?	$[(406/3, 7802/3)]$
453299.g1	453299g1	453299.g	453299g	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{6} \cdot 11 \cdot 29^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$7.313359348$	$1$		$2$	$8769600$	$2.098358$	$783/11$	$0.71531$	$3.71800$	$[1, -1, 1, 74691, 37887168]$	\(y^2+xy+y=x^3-x^2+74691x+37887168\)	22.2.0.a.1	$[(1249, 44965)]$
453299.h1	453299h1	453299.h	453299h	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{4} \cdot 11 \cdot 29^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$44$	$2$	$0$	$1$	$4$	$2$	$0$	$9375120$	$2.362892$	$41209/11$	$0.73251$	$3.99891$	$[1, 0, 0, -722016, 173263789]$	\(y^2+xy=x^3-722016x+173263789\)	44.2.0.a.1	$[]$
453299.i1	453299i1	453299.i	453299i	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{10} \cdot 11 \cdot 29^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$44$	$2$	$0$	$142.1974966$	$1$		$0$	$65625840$	$3.335846$	$41209/11$	$0.73251$	$4.89534$	$[1, 1, 1, -35378785, -59464858412]$	\(y^2+xy+y=x^3+x^2-35378785x-59464858412\)	44.2.0.a.1	$[(53975317710145335421276670087094966203683597275234113145209413/30242141984427992848603318652, 393656520087081467166898589940039121325553322769009346999122602640676900363407144308198077091/30242141984427992848603318652)]$
453299.j1	453299j2	453299.j	453299j	$2$	$2$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{12} \cdot 11 \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$4$	$2$	$0$	$13934592$	$2.570583$	$15124197817/1294139$	$0.97750$	$4.24735$	$[1, 1, 1, -2123122, -1100057204]$	\(y^2+xy+y=x^3+x^2-2123122x-1100057204\)	2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.?	$[]$
453299.j2	453299j1	453299.j	453299j	$2$	$2$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{9} \cdot 11^{2} \cdot 29^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$6967296$	$2.224010$	$4657463/41503$	$0.89262$	$3.83132$	$[1, 1, 1, 143373, -79227856]$	\(y^2+xy+y=x^3+x^2+143373x-79227856\)	2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.?	$[]$
453299.k1	453299k1	453299.k	453299k	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{8} \cdot 11 \cdot 29^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$4.214318119$	$1$		$2$	$4300800$	$1.869949$	$884736/539$	$1.02512$	$3.49902$	$[0, 0, 1, 82418, -2091357]$	\(y^2+y=x^3+82418x-2091357\)	22.2.0.a.1	$[(13601, 1586546)]$
453299.l1	453299l1	453299.l	453299l	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{7} \cdot 11 \cdot 29^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$154$	$2$	$0$	$1$	$1$		$0$	$6848640$	$2.322727$	$950272/77$	$0.67501$	$4.02158$	$[0, 1, 1, -796707, 253563174]$	\(y^2+y=x^3+x^2-796707x+253563174\)	154.2.0.?	$[]$
453299.m1	453299m1	453299.m	453299m	$3$	$9$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{8} \cdot 11 \cdot 29^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$40194$	$144$	$3$	$21.94139216$	$1$		$0$	$7741440$	$2.361603$	$-78843215872/539$	$1.00604$	$4.37413$	$[0, 1, 1, -3681337, -2719913430]$	\(y^2+y=x^3+x^2-3681337x-2719913430\)	3.4.0.a.1, 9.12.0.a.1, 22.2.0.a.1, 63.36.0.e.1, 66.8.0.a.1, $\ldots$	$[(684292495861/1350, 566053606743786109/1350)]$
453299.m2	453299m2	453299.m	453299m	$3$	$9$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{12} \cdot 11^{3} \cdot 29^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$40194$	$144$	$3$	$7.313797388$	$1$		$0$	$23224320$	$2.910908$	$-13278380032/156590819$	$1.06522$	$4.47248$	$[0, 1, 1, -2032977, -5159280185]$	\(y^2+y=x^3+x^2-2032977x-5159280185\)	3.12.0.a.1, 22.2.0.a.1, 63.36.0.b.1, 66.24.1.b.1, 609.24.0.?, $\ldots$	$[(1108069/18, 974136635/18)]$
453299.m3	453299m3	453299.m	453299m	$3$	$9$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{8} \cdot 11^{9} \cdot 29^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$40194$	$144$	$3$	$2.437932462$	$1$		$0$	$69672960$	$3.460217$	$9463555063808/115539436859$	$1.06593$	$4.97211$	$[0, 1, 1, 18159433, 133532287900]$	\(y^2+y=x^3+x^2+18159433x+133532287900\)	3.4.0.a.1, 9.12.0.a.1, 22.2.0.a.1, 63.36.0.e.2, 66.8.0.a.1, $\ldots$	$[(50950/3, 17451998/3)]$
453299.n1	453299n1	453299.n	453299n	$2$	$3$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{7} \cdot 11^{2} \cdot 29^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1218$	$16$	$0$	$6.102208065$	$1$		$0$	$13547520$	$2.759678$	$-28094464000/20657483$	$0.84860$	$4.35786$	$[0, 1, 1, -2609903, -2446285670]$	\(y^2+y=x^3+x^2-2609903x-2446285670\)	3.4.0.a.1, 6.8.0-3.a.1.1, 406.2.0.?, 609.8.0.?, 1218.16.0.?	$[(801133/18, 460095569/18)]$
453299.n2	453299n2	453299.n	453299n	$2$	$3$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{9} \cdot 11^{6} \cdot 29^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1218$	$16$	$0$	$2.034069355$	$1$		$0$	$40642560$	$3.308983$	$15252992000000/17621717267$	$0.97270$	$4.77838$	$[0, 1, 1, 21291317, 37751981187]$	\(y^2+y=x^3+x^2+21291317x+37751981187\)	3.4.0.a.1, 6.8.0-3.a.1.2, 406.2.0.?, 609.8.0.?, 1218.16.0.?	$[(56431/3, 17451998/3)]$
453299.o1	453299o1	453299.o	453299o	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{7} \cdot 11 \cdot 29^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$154$	$2$	$0$	$1$	$1$		$0$	$236160$	$0.639078$	$950272/77$	$0.67501$	$2.47035$	$[0, -1, 1, -947, 10723]$	\(y^2+y=x^3-x^2-947x+10723\)	154.2.0.?	$[]$
453299.p1	453299p1	453299.p	453299p	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{10} \cdot 11 \cdot 29^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$44$	$2$	$0$	$7.087196670$	$1$		$0$	$2262960$	$1.652199$	$41209/11$	$0.73251$	$3.34411$	$[1, 0, 1, -42068, -2441085]$	\(y^2+xy+y=x^3-42068x-2441085\)	44.2.0.a.1	$[(9501/4, 844499/4)]$
453299.q1	453299q4	453299.q	453299q	$4$	$4$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{9} \cdot 11^{8} \cdot 29^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.14	2B	$1624$	$48$	$0$	$15.56142664$	$1$		$0$	$216760320$	$4.044128$	$16798320881842096017/2132227789307$	$0.97557$	$5.84653$	$[1, -1, 0, -2198734526, -39678354903811]$	\(y^2+xy=x^3-x^2-2198734526x-39678354903811\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 28.12.0-4.c.1.2, 56.24.0-56.z.1.15, $\ldots$	$[(271313884/65, 2507186232543/65)]$
453299.q2	453299q3	453299.q	453299q	$4$	$4$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{18} \cdot 11^{2} \cdot 29^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.14	2B	$1624$	$48$	$0$	$15.56142664$	$1$		$0$	$216760320$	$4.044128$	$1048626554636928177/48569076788309$	$0.99097$	$5.63356$	$[1, -1, 0, -872216816, 9509994947767]$	\(y^2+xy=x^3-x^2-872216816x+9509994947767\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 28.12.0-4.c.1.1, 56.24.0-56.z.1.7, $\ldots$	$[(-21772119/64, 981410406773/64)]$
453299.q3	453299q2	453299.q	453299q	$4$	$4$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{12} \cdot 11^{4} \cdot 29^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.2	2Cs	$812$	$48$	$0$	$31.12285328$	$1$		$2$	$108380160$	$3.697552$	$5249244962308257/1448621666569$	$0.97197$	$5.22685$	$[1, -1, 0, -149204911, -507334996008]$	\(y^2+xy=x^3-x^2-149204911x-507334996008\)	2.6.0.a.1, 4.12.0-2.a.1.2, 28.24.0-28.b.1.4, 116.24.0.?, 812.48.0.?	$[(3640804203195864/474695, 121081308245691586652172/474695)]$
453299.q4	453299q1	453299.q	453299q	$4$	$4$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{9} \cdot 11^{2} \cdot 29^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.14	2B	$1624$	$48$	$0$	$15.56142664$	$1$		$1$	$54190080$	$3.350979$	$22062729659823/29354283343$	$0.91629$	$4.82681$	$[1, -1, 0, 24078934, -51841081041]$	\(y^2+xy=x^3-x^2+24078934x-51841081041\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 14.6.0.b.1, 28.12.0.g.1, $\ldots$	$[(4938349250/167, 346753062184761/167)]$
453299.r1	453299r1	453299.r	453299r	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{4} \cdot 11 \cdot 29^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$44$	$2$	$0$	$7.100430003$	$1$		$2$	$323280$	$0.679243$	$41209/11$	$0.73251$	$2.44767$	$[1, 1, 0, -858, 6749]$	\(y^2+xy=x^3+x^2-858x+6749\)	44.2.0.a.1	$[(95/2, 79/2), (76/3, 263/3)]$
453299.s1	453299s1	453299.s	453299s	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{6} \cdot 11 \cdot 29^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$10.38330407$	$1$		$0$	$302400$	$0.414709$	$783/11$	$0.71531$	$2.16676$	$[1, -1, 0, 89, 1532]$	\(y^2+xy=x^3-x^2+89x+1532\)	22.2.0.a.1	$[(-15329/42, 823019/42)]$
453299.t1	453299t1	453299.t	453299t	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{7} \cdot 11^{2} \cdot 29^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$406$	$2$	$0$	$1$	$1$		$0$	$51136512$	$2.741737$	$110592/847$	$0.70944$	$4.30725$	$[0, 0, 1, 1195061, -1758831027]$	\(y^2+y=x^3+1195061x-1758831027\)	406.2.0.?	$[]$
453299.u1	453299u1	453299.u	453299u	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{9} \cdot 11^{3} \cdot 29^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$154$	$2$	$0$	$4.800095466$	$1$		$0$	$3487680$	$1.686426$	$24395739136/1331$	$0.87868$	$3.69812$	$[0, 1, 1, -195624, -33366567]$	\(y^2+y=x^3+x^2-195624x-33366567\)	154.2.0.?	$[(10109/2, 999841/2)]$
453299.v1	453299v3	453299.v	453299v	$3$	$25$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{6} \cdot 11 \cdot 29^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.2	5B.4.2	$111650$	$1200$	$37$	$1$	$1$		$0$	$45360000$	$3.153313$	$-52893159101157376/11$	$1.09296$	$5.40422$	$[0, -1, 1, -322268116, 2226871079383]$	\(y^2+y=x^3-x^2-322268116x+2226871079383\)	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 110.24.1.?, 275.300.12.?, $\ldots$	$[]$
453299.v2	453299v2	453299.v	453299v	$3$	$25$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{6} \cdot 11^{5} \cdot 29^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.60.0.1	5Cs.4.1	$111650$	$1200$	$37$	$1$	$1$		$0$	$9072000$	$2.348595$	$-122023936/161051$	$1.01300$	$3.96850$	$[0, -1, 1, -425826, 193863543]$	\(y^2+y=x^3-x^2-425826x+193863543\)	5.60.0.a.1, 22.2.0.a.1, 110.120.5.?, 275.300.12.?, 550.600.37.?, $\ldots$	$[]$
453299.v3	453299v1	453299.v	453299v	$3$	$25$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( - 7^{6} \cdot 11 \cdot 29^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.1	5B.4.1	$111650$	$1200$	$37$	$1$	$1$		$0$	$1814400$	$1.543875$	$-4096/11$	$0.82546$	$3.21913$	$[0, -1, 1, -13736, -1467117]$	\(y^2+y=x^3-x^2-13736x-1467117\)	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 110.24.1.?, 275.300.12.?, $\ldots$	$[]$
453299.w1	453299w1	453299.w	453299w	$1$	$1$	\( 7^{2} \cdot 11 \cdot 29^{2} \)	\( 7^{3} \cdot 11^{3} \cdot 29^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$154$	$2$	$0$	$3.638817265$	$1$		$0$	$498240$	$0.713470$	$24395739136/1331$	$0.87868$	$2.80168$	$[0, -1, 1, -3992, 98419]$	\(y^2+y=x^3-x^2-3992x+98419\)	154.2.0.?	$[(553/4, 1453/4)]$