Elliptic curves over $\Q$ of conductor 31734

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (22 matches)

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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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
31734.a1	31734h1	31734.a	31734h	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2 \cdot 3^{7} \cdot 41 \cdot 43^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$984$	$2$	$0$	$1$	$1$		$0$	$410368$	$1.983868$	$-4617711815194147190977/454854$	$0.98126$	$5.44863$	$1$	$[1, -1, 0, -3122316, -2122774034]$	\(y^2+xy=x^3-x^2-3122316x-2122774034\)	984.2.0.?	$[ ]$	$1$
31734.b1	31734i1	31734.b	31734i	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{11} \cdot 3^{14} \cdot 41 \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$14104$	$2$	$0$	$1$	$1$		$0$	$78848$	$1.229359$	$-11779205551777/23689304064$	$0.90025$	$3.68423$	$1$	$[1, -1, 0, -4266, 227956]$	\(y^2+xy=x^3-x^2-4266x+227956\)	14104.2.0.?	$[ ]$	$1$
31734.c1	31734a1	31734.c	31734a	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{4} \cdot 3^{3} \cdot 41^{2} \cdot 43 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$516$	$2$	$0$	$0.356026559$	$1$		$14$	$12032$	$0.134078$	$-1187648379/1156528$	$0.83613$	$2.42909$	$1$	$[1, -1, 0, -66, 356]$	\(y^2+xy=x^3-x^2-66x+356\)	516.2.0.?	$[(-1, 21), (40, 226)]$	$1$
31734.d1	31734c1	31734.d	31734c	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{30} \cdot 3^{6} \cdot 41 \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3526$	$2$	$0$	$1$	$1$		$0$	$151200$	$1.584663$	$28717273414367/1893006835712$	$0.95382$	$4.08164$	$1$	$[1, -1, 0, 5742, 1778004]$	\(y^2+xy=x^3-x^2+5742x+1778004\)	3526.2.0.?	$[ ]$	$1$
31734.e1	31734g2	31734.e	31734g	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{8} \cdot 3^{10} \cdot 41^{6} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$7052$	$12$	$0$	$1$	$1$		$0$	$737280$	$2.282913$	$40648574705672938753/4235420946279168$	$0.96491$	$4.99204$	$1$	$[1, -1, 0, -644688, -180251136]$	\(y^2+xy=x^3-x^2-644688x-180251136\)	2.3.0.a.1, 164.6.0.?, 172.6.0.?, 7052.12.0.?	$[ ]$	$1$
31734.e2	31734g1	31734.e	31734g	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{16} \cdot 3^{8} \cdot 41^{3} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$7052$	$12$	$0$	$1$	$1$		$1$	$368640$	$1.936340$	$505151404935443713/75164179562496$	$0.98277$	$4.56871$	$1$	$[1, -1, 0, -149328, 19180800]$	\(y^2+xy=x^3-x^2-149328x+19180800\)	2.3.0.a.1, 82.6.0.?, 172.6.0.?, 7052.12.0.?	$[ ]$	$1$
31734.f1	31734f1	31734.f	31734f	$2$	$3$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{12} \cdot 3^{6} \cdot 41 \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$10578$	$16$	$0$	$1$	$1$		$0$	$20160$	$0.781417$	$-6713831364625/7221248$	$0.98495$	$3.48560$	$1$	$[1, -1, 0, -3537, -80163]$	\(y^2+xy=x^3-x^2-3537x-80163\)	3.8.0-3.a.1.1, 3526.2.0.?, 10578.16.0.?	$[ ]$	$1$
31734.f2	31734f2	31734.f	31734f	$2$	$3$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{4} \cdot 3^{6} \cdot 41^{3} \cdot 43^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$10578$	$16$	$0$	$1$	$1$		$2$	$60480$	$1.330723$	$12771880859375/87675231152$	$1.00811$	$3.77759$	$1$	$[1, -1, 0, 4383, -369171]$	\(y^2+xy=x^3-x^2+4383x-369171\)	3.8.0-3.a.1.2, 3526.2.0.?, 10578.16.0.?	$[ ]$	$1$
31734.g1	31734b1	31734.g	31734b	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{3} \cdot 3^{6} \cdot 41 \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$14104$	$2$	$0$	$1$	$1$		$0$	$8640$	$0.122385$	$-454756609/14104$	$0.77156$	$2.56428$	$1$	$[1, -1, 0, -144, -648]$	\(y^2+xy=x^3-x^2-144x-648\)	14104.2.0.?	$[ ]$	$1$
31734.h1	31734e1	31734.h	31734e	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{6} \cdot 3^{9} \cdot 41 \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$42312$	$12$	$0$	$10.69023521$	$1$		$1$	$29952$	$0.894851$	$106989222612817/3046464$	$0.89271$	$3.75252$	$1$	$[1, -1, 0, -8901, -321003]$	\(y^2+xy=x^3-x^2-8901x-321003\)	2.3.0.a.1, 8.6.0.d.1, 10578.6.0.?, 42312.12.0.?	$[(130419/5, 46761768/5)]$	$1$
31734.h2	31734e2	31734.h	31734e	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{3} \cdot 3^{12} \cdot 41^{2} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$42312$	$12$	$0$	$5.345117608$	$1$		$2$	$59904$	$1.241425$	$-94525928327377/18126841608$	$0.89620$	$3.76818$	$1$	$[1, -1, 0, -8541, -348435]$	\(y^2+xy=x^3-x^2-8541x-348435\)	2.3.0.a.1, 8.6.0.a.1, 21156.6.0.?, 42312.12.0.?	$[(20865, 3003375)]$	$1$
31734.i1	31734d1	31734.i	31734d	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{5} \cdot 3^{7} \cdot 41 \cdot 43^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$984$	$2$	$0$	$2.730596433$	$1$		$0$	$74240$	$1.205153$	$-40767965189713/13456400736$	$0.89278$	$3.70298$	$1$	$[1, -1, 0, -6453, -248427]$	\(y^2+xy=x^3-x^2-6453x-248427\)	984.2.0.?	$[(579/2, 10257/2)]$	$1$
31734.j1	31734k1	31734.j	31734k	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{10} \cdot 3^{11} \cdot 41^{2} \cdot 43^{3} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$516$	$2$	$0$	$0.115746227$	$1$		$28$	$441600$	$1.834404$	$-19178458591950217/33256712070144$	$0.94357$	$4.38678$	$1$	$[1, -1, 1, -50189, 8664117]$	\(y^2+xy+y=x^3-x^2-50189x+8664117\)	516.2.0.?	$[(-79, 3522), (-165, 3608)]$	$1$
31734.k1	31734p1	31734.k	31734p	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{18} \cdot 3^{11} \cdot 41 \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$42312$	$12$	$0$	$1$	$1$		$1$	$195840$	$1.569782$	$74202895742358313/112304848896$	$0.93297$	$4.38366$	$1$	$[1, -1, 1, -78791, -8481729]$	\(y^2+xy+y=x^3-x^2-78791x-8481729\)	2.3.0.a.1, 8.6.0.d.1, 10578.6.0.?, 42312.12.0.?	$[ ]$	$1$
31734.k2	31734p2	31734.k	31734p	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{9} \cdot 3^{16} \cdot 41^{2} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$42312$	$12$	$0$	$1$	$1$		$0$	$391680$	$1.916355$	$-26287353527251753/93969546895872$	$0.95259$	$4.47369$	$1$	$[1, -1, 1, -55751, -13559745]$	\(y^2+xy+y=x^3-x^2-55751x-13559745\)	2.3.0.a.1, 8.6.0.a.1, 21156.6.0.?, 42312.12.0.?	$[ ]$	$1$
31734.l1	31734m1	31734.l	31734m	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2 \cdot 3^{10} \cdot 41^{5} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$14104$	$2$	$0$	$1$	$1$		$0$	$115200$	$1.522728$	$1197736492998599/807054296166$	$0.93498$	$3.98556$	$1$	$[1, -1, 1, 19912, 433473]$	\(y^2+xy+y=x^3-x^2+19912x+433473\)	14104.2.0.?	$[ ]$	$1$
31734.m1	31734l1	31734.m	31734l	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{2} \cdot 3^{17} \cdot 41^{2} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$516$	$2$	$0$	$1$	$1$		$0$	$98560$	$1.293520$	$85131738691271/51218866404$	$0.93404$	$3.73047$	$1$	$[1, -1, 1, 8248, 55343]$	\(y^2+xy+y=x^3-x^2+8248x+55343\)	516.2.0.?	$[ ]$	$1$
31734.n1	31734o2	31734.n	31734o	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{3} \cdot 3^{6} \cdot 41^{2} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$328$	$12$	$0$	$1$	$1$		$0$	$147456$	$1.743717$	$54301858899649619257/24865352$	$0.96408$	$5.01998$	$1$	$[1, -1, 1, -710024, 230458115]$	\(y^2+xy+y=x^3-x^2-710024x+230458115\)	2.3.0.a.1, 8.6.0.b.1, 164.6.0.?, 328.12.0.?	$[ ]$	$1$
31734.n2	31734o1	31734.n	31734o	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{6} \cdot 3^{6} \cdot 41 \cdot 43^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$328$	$12$	$0$	$1$	$1$		$1$	$73728$	$1.397144$	$13263750031719097/8970933824$	$0.92342$	$4.21755$	$1$	$[1, -1, 1, -44384, 3608003]$	\(y^2+xy+y=x^3-x^2-44384x+3608003\)	2.3.0.a.1, 8.6.0.c.1, 82.6.0.?, 328.12.0.?	$[ ]$	$1$
31734.o1	31734n2	31734.o	31734n	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{10} \cdot 3^{22} \cdot 41^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$7052$	$12$	$0$	$1$	$1$		$0$	$737280$	$2.409863$	$1537276934430978316057/3186223241260032$	$1.17121$	$5.34252$	$1$	$[1, -1, 1, -2163974, 1223598741]$	\(y^2+xy+y=x^3-x^2-2163974x+1223598741\)	2.3.0.a.1, 164.6.0.?, 172.6.0.?, 7052.12.0.?	$[ ]$	$1$
31734.o2	31734n1	31734.o	31734n	$2$	$2$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( 2^{20} \cdot 3^{14} \cdot 41 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$7052$	$12$	$0$	$1$	$1$		$1$	$368640$	$2.063290$	$922625101256316697/521543718273024$	$0.98829$	$4.62682$	$1$	$[1, -1, 1, -182534, 4616853]$	\(y^2+xy+y=x^3-x^2-182534x+4616853\)	2.3.0.a.1, 82.6.0.?, 172.6.0.?, 7052.12.0.?	$[ ]$	$1$
31734.p1	31734j1	31734.p	31734j	$1$	$1$	\( 2 \cdot 3^{2} \cdot 41 \cdot 43 \)	\( - 2^{4} \cdot 3^{9} \cdot 41^{2} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$516$	$2$	$0$	$1$	$1$		$0$	$36096$	$0.683385$	$-1187648379/1156528$	$0.83613$	$3.06504$	$1$	$[1, -1, 1, -596, -9017]$	\(y^2+xy+y=x^3-x^2-596x-9017\)	516.2.0.?	$[ ]$	$1$

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