Elliptic curves over Q\Q of conductor 37845

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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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
37845.a1	37845a1	37845.a	37845a	$1$	$1$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{9} \cdot 5 \cdot 29^{7}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$870$	$2$	$0$	$1.167693465$	$1$		$2$	$201600$	$1.608206$	$110592/145$	$0.73528$	$3.97870$	$[0, 0, 1, 22707, -1481632]$	$y^2+y=x^3+22707x-1481632$	870.2.0.?	$[(1044, 34060)]$
37845.b1	37845f1	37845.b	37845f	$1$	$1$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{7} \cdot 5^{2} \cdot 29^{2}$	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.441201069$	$1$		$16$	$14400$	$0.159336$	$118784/75$	$0.81570$	$2.37271$	$[0, 0, 1, 87, 94]$	$y^2+y=x^3+87x+94$	6.2.0.a.1	$[(4, 22), (-1, 2)]$
37845.c1	37845e4	37845.c	37845e	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{8} \cdot 5 \cdot 29^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.10	2B	$6960$	$192$	$3$	$1$	$1$		$0$	$2150400$	$2.777073$	$37286818682653441/1305$	$1.23338$	$6.16178$	$[1, -1, 1, -52680398, 147183980316]$	$y^2+xy+y=x^3-x^2-52680398x+147183980316$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 48.24.0.j.1, 60.12.0-4.c.1.1, $\ldots$	$[]$
37845.c2	37845e2	37845.c	37845e	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{10} \cdot 5^{2} \cdot 29^{8}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.4	2Cs	$3480$	$192$	$3$	$1$	$1$		$2$	$1075200$	$2.430500$	$9104453457841/1703025$	$1.03605$	$5.37272$	$[1, -1, 1, -3292673, 2300150256]$	$y^2+xy+y=x^3-x^2-3292673x+2300150256$	2.6.0.a.1, 4.12.0.a.1, 24.24.0.j.1, 40.24.0-4.a.1.5, 60.24.0-4.a.1.2, $\ldots$	$[]$
37845.c3	37845e3	37845.c	37845e	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{8} \cdot 5^{4} \cdot 29^{10}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.9	2B	$6960$	$192$	$3$	$1$	$1$		$0$	$2150400$	$2.777073$	$-6561258219361/3978455625$	$0.95298$	$5.40964$	$[1, -1, 1, -2952068, 2794436232]$	$y^2+xy+y=x^3-x^2-2952068x+2794436232$	2.3.0.a.1, 4.12.0.d.1, 24.24.0.z.1, 40.24.0-4.d.1.5, 120.48.0.?, $\ldots$	$[]$
37845.c4	37845e1	37845.c	37845e	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{14} \cdot 5 \cdot 29^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.10	2B	$6960$	$192$	$3$	$1$	$1$		$1$	$537600$	$2.083927$	$2992209121/951345$	$0.88867$	$4.61185$	$[1, -1, 1, -227228, 28042422]$	$y^2+xy+y=x^3-x^2-227228x+28042422$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 48.24.0.j.1, 60.12.0-4.c.1.2, $\ldots$	$[]$
37845.d1	37845d8	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{10} \cdot 5 \cdot 29^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.121	2B	$13920$	$768$	$13$	$1$	$1$		$0$	$802816$	$2.523823$	$1114544804970241/405$	$1.07354$	$5.82878$	$[1, -1, 1, -16349198, 25448520512]$	$y^2+xy+y=x^3-x^2-16349198x+25448520512$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$	$[]$
37845.d2	37845d6	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{14} \cdot 5^{2} \cdot 29^{6}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.123	2Cs	$6960$	$768$	$13$	$1$	$1$		$2$	$401408$	$2.177250$	$272223782641/164025$	$1.03897$	$5.03976$	$[1, -1, 1, -1021973, 397703972]$	$y^2+xy+y=x^3-x^2-1021973x+397703972$	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$	$[]$
37845.d3	37845d7	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{22} \cdot 5 \cdot 29^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.134	2B	$13920$	$768$	$13$	$1$	$1$		$0$	$802816$	$2.523823$	$-147281603041/215233605$	$1.05949$	$5.10101$	$[1, -1, 1, -832748, 549386732]$	$y^2+xy+y=x^3-x^2-832748x+549386732$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$	$[]$
37845.d4	37845d4	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{7} \cdot 5 \cdot 29^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$13920$	$768$	$13$	$1$	$4$	$2$	$0$	$200704$	$1.830677$	$56667352321/15$	$1.03019$	$4.89087$	$[1, -1, 1, -605678, -181279114]$	$y^2+xy+y=x^3-x^2-605678x-181279114$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$	$[]$
37845.d5	37845d3	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{10} \cdot 5^{4} \cdot 29^{6}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.44	2Cs	$6960$	$768$	$13$	$1$	$1$		$2$	$200704$	$1.830677$	$111284641/50625$	$1.02534$	$4.29959$	$[1, -1, 1, -75848, 3737522]$	$y^2+xy+y=x^3-x^2-75848x+3737522$	2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$	$[]$
37845.d6	37845d2	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{8} \cdot 5^{2} \cdot 29^{6}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.3	2Cs	$6960$	$768$	$13$	$1$	$1$		$2$	$100352$	$1.484102$	$13997521/225$	$0.96230$	$4.10291$	$[1, -1, 1, -38003, -2802094]$	$y^2+xy+y=x^3-x^2-38003x-2802094$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$	$[]$
37845.d7	37845d1	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{7} \cdot 5 \cdot 29^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$13920$	$768$	$13$	$1$	$1$		$1$	$50176$	$1.137529$	$-1/15$	$1.19808$	$3.50606$	$[1, -1, 1, -158, -122668]$	$y^2+xy+y=x^3-x^2-158x-122668$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$	$[]$
37845.d8	37845d5	37845.d	37845d	$8$	$16$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{8} \cdot 5^{8} \cdot 29^{6}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.197	2B	$13920$	$768$	$13$	$1$	$1$		$0$	$401408$	$2.177250$	$4733169839/3515625$	$1.05585$	$4.65536$	$[1, -1, 1, 264757, 27852356]$	$y^2+xy+y=x^3-x^2+264757x+27852356$	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$	$[]$
37845.e1	37845j1	37845.e	37845j	$2$	$2$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{6} \cdot 5 \cdot 29^{7}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$3480$	$48$	$0$	$1.658476194$	$1$		$3$	$107520$	$1.396452$	$2146689/145$	$0.84440$	$3.92504$	$[1, -1, 1, -20342, -1044404]$	$y^2+xy+y=x^3-x^2-20342x-1044404$	2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 290.6.0.?, 580.24.0.?, $\ldots$	$[(979, 29786)]$
37845.e2	37845j2	37845.e	37845j	$2$	$2$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{6} \cdot 5^{2} \cdot 29^{8}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$3480$	$48$	$0$	$3.316952389$	$1$		$0$	$215040$	$1.743027$	$1367631/21025$	$0.96200$	$4.18975$	$[1, -1, 1, 17503, -4511006]$	$y^2+xy+y=x^3-x^2+17503x-4511006$	2.3.0.a.1, 4.6.0.a.1, 120.12.0.?, 580.12.0.?, 696.12.0.?, $\ldots$	$[(3887/2, 239999/2)]$
37845.f1	37845i1	37845.f	37845i	$1$	$1$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{11} \cdot 5^{7} \cdot 29^{7}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$870$	$2$	$0$	$0.738347201$	$1$		$4$	$940800$	$2.591248$	$53838872576/550546875$	$1.03969$	$5.15293$	$[0, 0, 1, 595428, 722042442]$	$y^2+y=x^3+595428x+722042442$	870.2.0.?	$[(6032, 473062)]$
37845.g1	37845h1	37845.g	37845h	$2$	$3$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{9} \cdot 5 \cdot 29^{7}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$870$	$16$	$0$	$5.245176868$	$1$		$0$	$134400$	$1.707781$	$-160989184/3915$	$0.86981$	$4.33852$	$[0, 0, 1, -85782, -9871448]$	$y^2+y=x^3-85782x-9871448$	3.4.0.a.1, 30.8.0-3.a.1.1, 87.8.0.?, 870.16.0.?	$[(29290/7, 4234684/7)]$
37845.g2	37845h2	37845.g	37845h	$2$	$3$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{7} \cdot 5^{3} \cdot 29^{9}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$870$	$16$	$0$	$1.748392289$	$1$		$4$	$403200$	$2.257088$	$12747309056/9145875$	$0.97110$	$4.74934$	$[0, 0, 1, 368358, -42138095]$	$y^2+y=x^3+368358x-42138095$	3.4.0.a.1, 30.8.0-3.a.1.2, 87.8.0.?, 870.16.0.?	$[(145, 3784)]$
37845.h1	37845c4	37845.h	37845c	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{8} \cdot 5 \cdot 29^{10}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3480$	$48$	$0$	$1$	$9$	$3$	$0$	$1290240$	$2.470604$	$1888690601881/31827645$	$0.93261$	$5.22351$	$[1, -1, 0, -1949175, 1032552796]$	$y^2+xy=x^3-x^2-1949175x+1032552796$	2.3.0.a.1, 4.6.0.c.1, 10.6.0.a.1, 20.12.0.g.1, 24.12.0-4.c.1.3, $\ldots$	$[]$
37845.h2	37845c2	37845.h	37845c	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{10} \cdot 5^{2} \cdot 29^{8}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1740$	$48$	$0$	$1$	$9$	$3$	$2$	$645120$	$2.124031$	$3803721481/1703025$	$0.90376$	$4.63462$	$[1, -1, 0, -246150, -22300889]$	$y^2+xy=x^3-x^2-246150x-22300889$	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 60.24.0-20.b.1.3, 116.12.0.?, $\ldots$	$[]$
37845.h3	37845c1	37845.h	37845c	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$3^{8} \cdot 5 \cdot 29^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3480$	$48$	$0$	$1$	$9$	$3$	$1$	$322560$	$1.777458$	$2305199161/1305$	$0.87163$	$4.58711$	$[1, -1, 0, -208305, -36523040]$	$y^2+xy=x^3-x^2-208305x-36523040$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.z.1, 120.24.0.?, $\ldots$	$[]$
37845.h4	37845c3	37845.h	37845c	$4$	$4$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{14} \cdot 5^{4} \cdot 29^{7}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$3480$	$48$	$0$	$1$	$9$	$3$	$0$	$1290240$	$2.470604$	$157376536199/118918125$	$0.94171$	$4.98777$	$[1, -1, 0, 851355, -167391050]$	$y^2+xy=x^3-x^2+851355x-167391050$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.z.1, 116.12.0.?, $\ldots$	$[]$
37845.i1	37845g1	37845.i	37845g	$1$	$1$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{7} \cdot 5^{2} \cdot 29^{8}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$3.985731744$	$1$		$0$	$417600$	$1.842983$	$118784/75$	$0.81570$	$4.28935$	$[0, 0, 1, 73167, 2298663]$	$y^2+y=x^3+73167x+2298663$	6.2.0.a.1	$[(841/6, 433007/6)]$
37845.j1	37845b1	37845.j	37845b	$1$	$1$	$3^{2} \cdot 5 \cdot 29^{2}$	$- 3^{3} \cdot 5 \cdot 29^{7}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$870$	$2$	$0$	$1$	$1$		$0$	$67200$	$1.058899$	$110592/145$	$0.73528$	$3.35338$	$[0, 0, 1, 2523, 54875]$	$y^2+y=x^3+2523x+54875$	870.2.0.?	$[]$

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