Elliptic curves over $\Q$ of conductor 45662

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

Results (32 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
45662.a1	45662j1	45662.a	45662j	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{2} \cdot 17^{4} \cdot 79 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$474$	$16$	$0$	$1.074295628$	$1$		$10$	$32832$	$0.513242$	$-8861981833/316$	$0.87447$	$3.19115$		$[1, 0, 1, -1885, 31332]$	\(y^2+xy+y=x^3-1885x+31332\)	3.8.0-3.a.1.2, 158.2.0.?, 474.16.0.?	$[(7, 132)]$	$1$
45662.a2	45662j2	45662.a	45662j	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{6} \cdot 17^{4} \cdot 79^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$474$	$16$	$0$	$0.358098542$	$1$		$8$	$98496$	$1.062548$	$-112425913/31554496$	$0.96402$	$3.36068$		$[1, 0, 1, -440, 78150]$	\(y^2+xy+y=x^3-440x+78150\)	3.8.0-3.a.1.1, 158.2.0.?, 474.16.0.?	$[(33, 299)]$	$1$
45662.b1	45662c3	45662.b	45662c	$3$	$9$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{18} \cdot 17^{6} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$48348$	$144$	$3$	$5.450392321$	$1$		$2$	$622080$	$2.096466$	$15698803397448457/20709376$	$1.00146$	$5.06026$		$[1, 1, 0, -1507574, -713096876]$	\(y^2+xy=x^3+x^2-1507574x-713096876\)	3.4.0.a.1, 9.12.0.a.1, 51.8.0-3.a.1.1, 153.24.0.?, 316.2.0.?, $\ldots$	$[(88860, 26441842)]$	$1$
45662.b2	45662c2	45662.b	45662c	$3$	$9$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{6} \cdot 17^{6} \cdot 79^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$48348$	$144$	$3$	$1.816797440$	$1$		$2$	$207360$	$1.547159$	$59914169497/31554496$	$0.96798$	$3.89742$		$[1, 1, 0, -23559, -427211]$	\(y^2+xy=x^3+x^2-23559x-427211\)	3.12.0.a.1, 51.24.0-3.a.1.1, 316.2.0.?, 711.36.0.?, 948.24.1.?, $\ldots$	$[(222, 2201)]$	$1$
45662.b3	45662c1	45662.b	45662c	$3$	$9$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{2} \cdot 17^{6} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$48348$	$144$	$3$	$0.605599146$	$1$		$4$	$69120$	$0.997852$	$11134383337/316$	$0.90937$	$3.74056$		$[1, 1, 0, -13444, 594404]$	\(y^2+xy=x^3+x^2-13444x+594404\)	3.4.0.a.1, 9.12.0.a.1, 51.8.0-3.a.1.2, 153.24.0.?, 316.2.0.?, $\ldots$	$[(86, 246)]$	$1$
45662.c1	45662b2	45662.c	45662b	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{9} \cdot 17^{2} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$32232$	$16$	$0$	$11.69609980$	$1$		$0$	$66096$	$1.016041$	$-15014675927571625/40448$	$0.95288$	$3.99983$		$[1, 1, 0, -33980, -2425136]$	\(y^2+xy=x^3+x^2-33980x-2425136\)	3.4.0.a.1, 51.8.0-3.a.1.1, 632.2.0.?, 1896.8.0.?, 32232.16.0.?	$[(119675/2, 41280861/2)]$	$1$
45662.c2	45662b1	45662.c	45662b	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{3} \cdot 17^{2} \cdot 79^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$32232$	$16$	$0$	$3.898699933$	$1$		$2$	$22032$	$0.466734$	$-25519101625/3944312$	$0.86005$	$2.78365$		$[1, 1, 0, -405, -3707]$	\(y^2+xy=x^3+x^2-405x-3707\)	3.4.0.a.1, 51.8.0-3.a.1.2, 632.2.0.?, 1896.8.0.?, 32232.16.0.?	$[(37, 165)]$	$1$
45662.d1	45662i1	45662.d	45662i	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{23} \cdot 17^{8} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$632$	$2$	$0$	$34.53791136$	$1$		$0$	$619344$	$2.260956$	$7913234375/662700032$	$0.99459$	$4.69990$		$[1, 1, 0, 79325, -103054579]$	\(y^2+xy=x^3+x^2+79325x-103054579\)	632.2.0.?	$[(869352621113225/653753, 25444980607247539344947/653753)]$	$1$
45662.e1	45662g1	45662.e	45662g	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{5} \cdot 17^{4} \cdot 79 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$632$	$2$	$0$	$1$	$1$		$0$	$25200$	$0.427184$	$334553625/2528$	$0.85683$	$2.88574$		$[1, -1, 0, -632, -5920]$	\(y^2+xy=x^3-x^2-632x-5920\)	632.2.0.?	$[ ]$	$1$
45662.f1	45662e1	45662.f	45662e	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{5} \cdot 17^{10} \cdot 79 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$632$	$2$	$0$	$1$	$9$	$3$	$0$	$428400$	$1.843790$	$334553625/2528$	$0.85683$	$4.47016$		$[1, -1, 0, -182702, -29815692]$	\(y^2+xy=x^3-x^2-182702x-29815692\)	632.2.0.?	$[ ]$	$1$
45662.g1	45662a1	45662.g	45662a	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{23} \cdot 17^{2} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$632$	$2$	$0$	$9.200882558$	$1$		$0$	$36432$	$0.844348$	$7913234375/662700032$	$0.99459$	$3.11548$		$[1, 0, 1, 274, -20960]$	\(y^2+xy+y=x^3+274x-20960\)	632.2.0.?	$[(8440/9, 740575/9)]$	$1$
45662.h1	45662h2	45662.h	45662h	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{9} \cdot 17^{8} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$1896$	$16$	$0$	$146.6513360$	$1$		$0$	$1123632$	$2.432648$	$-15014675927571625/40448$	$0.95288$	$5.58425$		$[1, 0, 1, -9820371, -11845950930]$	\(y^2+xy+y=x^3-9820371x-11845950930\)	3.8.0-3.a.1.1, 632.2.0.?, 1896.16.0.?	$[(4632929837554230228262223816353462965035730506295442210415167399/381507362358575125353604417890, 312870624314266517548695126321928250825851510448461526397570163100617028594817313723968150628613/381507362358575125353604417890)]$	$1$
45662.h2	45662h1	45662.h	45662h	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{3} \cdot 17^{8} \cdot 79^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$1896$	$16$	$0$	$48.88377868$	$1$		$2$	$374544$	$1.883341$	$-25519101625/3944312$	$0.86005$	$4.36807$		$[1, 0, 1, -117196, -17392478]$	\(y^2+xy+y=x^3-117196x-17392478\)	3.8.0-3.a.1.2, 632.2.0.?, 1896.16.0.?	$[(22241987988895504109708/6667504633, 2006358917429033317788842327318101/6667504633)]$	$1$
45662.i1	45662f1	45662.i	45662f	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{2} \cdot 17^{6} \cdot 79 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$1.670866576$	$1$		$8$	$39424$	$0.646042$	$4826809/316$	$0.94063$	$3.01882$		$[1, 0, 1, -1018, 11680]$	\(y^2+xy+y=x^3-1018x+11680\)	316.2.0.?	$[(-10, 149), (199/3, -23/3)]$	$1$
45662.j1	45662d1	45662.j	45662d	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{2} \cdot 17^{10} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$8058$	$16$	$0$	$9.154267190$	$1$		$0$	$558144$	$1.929848$	$-8861981833/316$	$0.87447$	$4.77557$		$[1, 1, 0, -544626, 154479968]$	\(y^2+xy=x^3+x^2-544626x+154479968\)	3.4.0.a.1, 51.8.0-3.a.1.2, 158.2.0.?, 474.8.0.?, 8058.16.0.?	$[(49592/11, 480532/11)]$	$1$
45662.j2	45662d2	45662.j	45662d	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{6} \cdot 17^{10} \cdot 79^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$8058$	$16$	$0$	$27.46280157$	$1$		$0$	$1674432$	$2.479156$	$-112425913/31554496$	$0.96402$	$4.94511$		$[1, 1, 0, -127021, 384079197]$	\(y^2+xy=x^3+x^2-127021x+384079197\)	3.4.0.a.1, 51.8.0-3.a.1.1, 158.2.0.?, 474.8.0.?, 8058.16.0.?	$[(2389937819322/1133, 3693353415664737159/1133)]$	$1$
45662.k1	45662s2	45662.k	45662s	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{11} \cdot 17^{10} \cdot 79^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$632$	$12$	$0$	$2.138106703$	$1$		$2$	$1216512$	$2.549831$	$126095937366490993/1067529340928$	$0.94200$	$5.25445$		$[1, 0, 0, -3019189, -2004647007]$	\(y^2+xy=x^3-3019189x-2004647007\)	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[(10122, 997191)]$	$1$
45662.k2	45662s1	45662.k	45662s	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{22} \cdot 17^{8} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$632$	$12$	$0$	$4.276213406$	$1$		$3$	$608256$	$2.203259$	$-981218819953/95760154624$	$0.94719$	$4.63649$		$[1, 0, 0, -59829, -73368671]$	\(y^2+xy=x^3-59829x-73368671\)	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[(754, 17239)]$	$1$
45662.l1	45662m2	45662.l	45662m	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{11} \cdot 17^{8} \cdot 79^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$136$	$12$	$0$	$1$	$1$		$0$	$3041280$	$2.719597$	$250505699702316625/23053462341632$	$0.99294$	$5.31843$		$[1, 0, 0, -3795443, 2609642593]$	\(y^2+xy=x^3-3795443x+2609642593\)	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[ ]$	$1$
45662.l2	45662m1	45662.l	45662m	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{22} \cdot 17^{7} \cdot 79^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$136$	$12$	$0$	$1$	$1$		$1$	$1520640$	$2.373024$	$2677801592364625/445003071488$	$0.92442$	$4.89542$		$[1, 0, 0, -836083, -248507295]$	\(y^2+xy=x^3-836083x-248507295\)	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[ ]$	$1$
45662.m1	45662r2	45662.m	45662r	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2 \cdot 17^{6} \cdot 79^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$632$	$12$	$0$	$4.263275245$	$1$		$0$	$61440$	$0.926141$	$81182737/12482$	$0.85973$	$3.28189$		$[1, 0, 0, -2607, 43687]$	\(y^2+xy=x^3-2607x+43687\)	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[(1167/2, 38137/2)]$	$1$
45662.m2	45662r1	45662.m	45662r	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{2} \cdot 17^{6} \cdot 79 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$632$	$12$	$0$	$8.526550491$	$1$		$1$	$30720$	$0.579567$	$103823/316$	$0.80009$	$2.79605$		$[1, 0, 0, 283, 3805]$	\(y^2+xy=x^3+283x+3805\)	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[(-842/17, 274357/17)]$	$1$
45662.n1	45662n1	45662.n	45662n	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{2} \cdot 17^{2} \cdot 79 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$158$	$2$	$0$	$1$	$1$		$0$	$6480$	$-0.359070$	$506447/316$	$0.74544$	$1.75241$		$[1, 0, 0, 11, -3]$	\(y^2+xy=x^3+11x-3\)	158.2.0.?	$[ ]$	$1$
45662.o1	45662q1	45662.o	45662q	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{6} \cdot 17^{8} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$1.033857724$	$1$		$4$	$165888$	$1.388302$	$67967263441/1461184$	$0.83809$	$3.90917$		$[1, 1, 1, -24571, 1444425]$	\(y^2+xy+y=x^3+x^2-24571x+1444425\)	316.2.0.?	$[(69, 254)]$	$1$
45662.p1	45662l2	45662.p	45662l	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{4} \cdot 17^{18} \cdot 79 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$16116$	$16$	$0$	$1$	$9$	$3$	$0$	$21897216$	$3.579849$	$7015012231880398928833/736434507858417904$	$1.02937$	$6.27286$		$[1, 1, 1, -115256674, -430953249921]$	\(y^2+xy+y=x^3+x^2-115256674x-430953249921\)	3.4.0.a.1, 51.8.0-3.a.1.1, 316.2.0.?, 948.8.0.?, 16116.16.0.?	$[ ]$	$1$
45662.p2	45662l1	45662.p	45662l	$2$	$3$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{12} \cdot 17^{10} \cdot 79^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$16116$	$16$	$0$	$1$	$1$		$0$	$7299072$	$3.030540$	$78311397007706818753/168669635866624$	$1.01300$	$5.85389$		$[1, 1, 1, -25759154, 50216102463]$	\(y^2+xy+y=x^3+x^2-25759154x+50216102463\)	3.4.0.a.1, 51.8.0-3.a.1.2, 316.2.0.?, 948.8.0.?, 16116.16.0.?	$[ ]$	$1$
45662.q1	45662k2	45662.q	45662k	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{13} \cdot 17^{12} \cdot 79^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$10744$	$12$	$0$	$1$	$1$		$0$	$2515968$	$3.022739$	$4991662883279390625/1234063918112768$	$1.11851$	$5.59730$		$[1, -1, 1, -10289755, -9612561141]$	\(y^2+xy+y=x^3-x^2-10289755x-9612561141\)	2.3.0.a.1, 8.6.0.b.1, 5372.6.0.?, 10744.12.0.?	$[ ]$	$1$
45662.q2	45662k1	45662.q	45662k	$2$	$2$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{26} \cdot 17^{9} \cdot 79 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$10744$	$12$	$0$	$1$	$1$		$1$	$1257984$	$2.676167$	$16985493417441375/26046762057728$	$1.00446$	$5.11427$		$[1, -1, 1, 1547685, -952290037]$	\(y^2+xy+y=x^3-x^2+1547685x-952290037\)	2.3.0.a.1, 8.6.0.c.1, 2686.6.0.?, 10744.12.0.?	$[ ]$	$1$
45662.r1	45662p2	45662.r	45662p	$2$	$5$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{4} \cdot 17^{6} \cdot 79^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$26860$	$48$	$1$	$2.152962904$	$1$		$4$	$1228800$	$2.558716$	$1413378216646643521/49232902384$	$1.01962$	$5.47970$		$[1, 0, 0, -6756826, -6760601228]$	\(y^2+xy=x^3-6756826x-6760601228\)	5.12.0.a.2, 85.24.0.?, 316.2.0.?, 1580.24.1.?, 26860.48.1.?	$[(-1506, 464)]$	$1$
45662.r2	45662p1	45662.r	45662p	$2$	$5$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{20} \cdot 17^{6} \cdot 79 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$26860$	$48$	$1$	$0.430592580$	$1$		$4$	$245760$	$1.753998$	$8194759433281/82837504$	$0.96131$	$4.35583$		$[1, 0, 0, -121386, 16125092]$	\(y^2+xy=x^3-121386x+16125092\)	5.12.0.a.1, 85.24.0.?, 316.2.0.?, 1580.24.1.?, 26860.48.1.?	$[(-44, 4646)]$	$1$
45662.s1	45662t1	45662.s	45662t	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( - 2^{2} \cdot 17^{8} \cdot 79 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$158$	$2$	$0$	$1$	$1$		$0$	$110160$	$1.057537$	$506447/316$	$0.74544$	$3.33683$		$[1, 1, 1, 3173, -17915]$	\(y^2+xy+y=x^3+x^2+3173x-17915\)	158.2.0.?	$[ ]$	$1$
45662.t1	45662o1	45662.t	45662o	$1$	$1$	\( 2 \cdot 17^{2} \cdot 79 \)	\( 2^{8} \cdot 17^{6} \cdot 79 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$316$	$2$	$0$	$1$	$1$		$0$	$147456$	$0.950029$	$72511713/20224$	$0.89606$	$3.27136$		$[1, -1, 1, -2511, 35479]$	\(y^2+xy+y=x^3-x^2-2511x+35479\)	316.2.0.?	$[ ]$	$1$

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