LMFDB - Elliptic curves over $\Q$ of conductor 2175

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Conductor	Discriminant	j-invariant	Rank

Bad $\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\$ div $\$ \|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax $\ \ell$	$abc$ quality	Szpiro ratio

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Results (21 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
2175.a1	2175j1	2175.a	2175j	$2$	$5$	$3 \cdot 5^{2} \cdot 29$	$- 3 \cdot 5^{3} \cdot 29$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.3	5B.1.2	$870$	$48$	$1$	$1$	$1$		$0$	$912$	$0.141300$	$-301302001664/87$	$1.19848$	$4.06774$	$[0, 1, 1, -698, -7336]$	$y^2+y=x^3+x^2-698x-7336$	5.24.0-5.a.2.2, 870.48.1.?	$[]$
2175.a2	2175j2	2175.a	2175j	$2$	$5$	$3 \cdot 5^{2} \cdot 29$	$- 3^{5} \cdot 5^{3} \cdot 29^{5}$	$0$	$\Z/5\Z$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.1	5B.1.1	$870$	$48$	$1$	$1$	$1$		$4$	$4560$	$0.946019$	$1351431663616/4984209207$	$1.01570$	$4.48183$	$[0, 1, 1, 1152, -34486]$	$y^2+y=x^3+x^2+1152x-34486$	5.24.0-5.a.1.2, 870.48.1.?	$[]$
2175.b1	2175c3	2175.b	2175c	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$3^{2} \cdot 5^{7} \cdot 29^{4}$	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$1160$	$48$	$0$	$0.482474972$	$1$		$24$	$4608$	$1.042370$	$1888690601881/31827645$	$0.93261$	$4.93489$	$[1, 1, 1, -6438, -198594]$	$y^2+xy+y=x^3+x^2-6438x-198594$	2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 232.24.0.?, $\ldots$	$[(-44, 65), (-50, 62)]$
2175.b2	2175c2	2175.b	2175c	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$3^{4} \cdot 5^{8} \cdot 29^{2}$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$580$	$48$	$0$	$1.929899890$	$1$		$24$	$2304$	$0.695796$	$3803721481/1703025$	$0.90376$	$4.12710$	$[1, 1, 1, -813, 3906]$	$y^2+xy+y=x^3+x^2-813x+3906$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 116.24.0.?, 580.48.0.?	$[(0, 62), (30, 72)]$
2175.b3	2175c1	2175.b	2175c	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$3^{2} \cdot 5^{7} \cdot 29$	$2$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1160$	$48$	$0$	$1.929899890$	$1$		$23$	$1152$	$0.349223$	$2305199161/1305$	$0.87163$	$4.06193$	$[1, 1, 1, -688, 6656]$	$y^2+xy+y=x^3+x^2-688x+6656$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 232.24.0.?, 290.6.0.?, $\ldots$	$[(14, -3), (11, 18)]$
2175.b4	2175c4	2175.b	2175c	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$- 3^{8} \cdot 5^{10} \cdot 29$	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1160$	$48$	$0$	$1.929899890$	$1$		$18$	$4608$	$1.042370$	$157376536199/118918125$	$0.94171$	$4.61152$	$[1, 1, 1, 2812, 32906]$	$y^2+xy+y=x^3+x^2+2812x+32906$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 40.24.0-40.z.1.10, $\ldots$	$[(20, 302), (9, 238)]$
2175.c1	2175e2	2175.c	2175e	$2$	$2$	$3 \cdot 5^{2} \cdot 29$	$3^{2} \cdot 5^{3} \cdot 29^{2}$	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$0.319074969$	$1$		$10$	$384$	$0.090849$	$12698260037/7569$	$0.91772$	$3.65567$	$[1, 1, 1, -243, 1356]$	$y^2+xy+y=x^3+x^2-243x+1356$	2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.?	$[(10, 2)]$
2175.c2	2175e1	2175.c	2175e	$2$	$2$	$3 \cdot 5^{2} \cdot 29$	$3^{4} \cdot 5^{3} \cdot 29$	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$0.638149939$	$1$		$7$	$192$	$-0.255725$	$5177717/2349$	$0.85504$	$2.64005$	$[1, 1, 1, -18, 6]$	$y^2+xy+y=x^3+x^2-18x+6$	2.3.0.a.1, 20.6.0.c.1, 116.6.0.?, 290.6.0.?, 580.12.0.?	$[(0, 2)]$
2175.d1	2175a1	2175.d	2175a	$2$	$3$	$3 \cdot 5^{2} \cdot 29$	$- 3^{3} \cdot 5^{7} \cdot 29$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$870$	$16$	$0$	$0.269557008$	$1$		$4$	$480$	$0.279546$	$-160989184/3915$	$0.86981$	$3.72094$	$[0, -1, 1, -283, 1968]$	$y^2+y=x^3-x^2-283x+1968$	3.4.0.a.1, 15.8.0-3.a.1.2, 174.8.0.?, 870.16.0.?	$[(12, 12)]$
2175.d2	2175a2	2175.d	2175a	$2$	$3$	$3 \cdot 5^{2} \cdot 29$	$- 3 \cdot 5^{9} \cdot 29^{3}$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$870$	$16$	$0$	$0.808671026$	$1$		$4$	$1440$	$0.828853$	$12747309056/9145875$	$0.97110$	$4.28447$	$[0, -1, 1, 1217, 7593]$	$y^2+y=x^3-x^2+1217x+7593$	3.4.0.a.1, 15.8.0-3.a.1.1, 174.8.0.?, 870.16.0.?	$[(-3, 62)]$
2175.e1	2175d1	2175.e	2175d	$1$	$1$	$3 \cdot 5^{2} \cdot 29$	$- 3^{7} \cdot 5^{8} \cdot 29^{2}$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$0.424252168$	$1$		$4$	$1680$	$1.011440$	$-15947530240/1839267$	$0.99256$	$4.75613$	$[0, -1, 1, -3833, 101318]$	$y^2+y=x^3-x^2-3833x+101318$	6.2.0.a.1	$[(-8, 362)]$
2175.f1	2175g1	2175.f	2175g	$1$	$1$	$3 \cdot 5^{2} \cdot 29$	$- 3^{7} \cdot 5^{2} \cdot 29^{2}$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$0.109229930$	$1$		$6$	$336$	$0.206722$	$-15947530240/1839267$	$0.99256$	$3.49954$	$[0, 1, 1, -153, 749]$	$y^2+y=x^3+x^2-153x+749$	6.2.0.a.1	$[(27, 130)]$
2175.g1	2175h1	2175.g	2175h	$1$	$1$	$3 \cdot 5^{2} \cdot 29$	$- 3^{5} \cdot 5^{13} \cdot 29$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$870$	$2$	$0$	$0.436544531$	$1$		$4$	$3360$	$1.163013$	$53838872576/550546875$	$1.03969$	$4.83807$	$[0, 1, 1, 1967, -136406]$	$y^2+y=x^3+x^2+1967x-136406$	870.2.0.?	$[(278, 4687)]$
2175.h1	2175b3	2175.h	2175b	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$3^{2} \cdot 5^{7} \cdot 29$	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.10	2B	$6960$	$192$	$3$	$1$	$4$	$2$	$0$	$7680$	$1.348839$	$37286818682653441/1305$	$1.23338$	$6.22191$	$[1, 1, 0, -174000, -28009125]$	$y^2+xy=x^3+x^2-174000x-28009125$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 20.12.0-4.c.1.1, 40.24.0-8.o.1.3, $\ldots$	$[]$
2175.h2	2175b2	2175.h	2175b	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$3^{4} \cdot 5^{8} \cdot 29^{2}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.4	2Cs	$3480$	$192$	$3$	$1$	$4$	$2$	$2$	$3840$	$1.002264$	$9104453457841/1703025$	$1.03605$	$5.13956$	$[1, 1, 0, -10875, -441000]$	$y^2+xy=x^3+x^2-10875x-441000$	2.6.0.a.1, 4.12.0.a.1, 20.24.0-4.a.1.1, 24.24.0.j.1, 116.24.0.?, $\ldots$	$[]$
2175.h3	2175b4	2175.h	2175b	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$- 3^{2} \cdot 5^{10} \cdot 29^{4}$	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.9	2B	$6960$	$192$	$3$	$1$	$1$		$0$	$7680$	$1.348839$	$-6561258219361/3978455625$	$0.95298$	$5.19020$	$[1, 1, 0, -9750, -534375]$	$y^2+xy=x^3+x^2-9750x-534375$	2.3.0.a.1, 4.12.0.d.1, 20.24.0-4.d.1.1, 24.24.0.z.1, 120.48.0.?, $\ldots$	$[]$
2175.h4	2175b1	2175.h	2175b	$4$	$4$	$3 \cdot 5^{2} \cdot 29$	$3^{8} \cdot 5^{7} \cdot 29$	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.10	2B	$6960$	$192$	$3$	$1$	$1$		$1$	$1920$	$0.655691$	$2992209121/951345$	$0.88867$	$4.09587$	$[1, 1, 0, -750, -5625]$	$y^2+xy=x^3+x^2-750x-5625$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 20.12.0-4.c.1.2, 40.24.0-8.o.1.1, $\ldots$	$[]$
2175.i1	2175i2	2175.i	2175i	$2$	$2$	$3 \cdot 5^{2} \cdot 29$	$3^{2} \cdot 5^{9} \cdot 29^{2}$	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$		$0$	$1920$	$0.895568$	$12698260037/7569$	$0.91772$	$4.91226$	$[1, 0, 1, -6076, 181673]$	$y^2+xy+y=x^3-6076x+181673$	2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.?	$[]$
2175.i2	2175i1	2175.i	2175i	$2$	$2$	$3 \cdot 5^{2} \cdot 29$	$3^{4} \cdot 5^{9} \cdot 29$	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$580$	$12$	$0$	$1$	$1$		$1$	$960$	$0.548994$	$5177717/2349$	$0.85504$	$3.89664$	$[1, 0, 1, -451, 1673]$	$y^2+xy+y=x^3-451x+1673$	2.3.0.a.1, 20.6.0.c.1, 116.6.0.?, 290.6.0.?, 580.12.0.?	$[]$
2175.j1	2175f1	2175.j	2175f	$2$	$5$	$3 \cdot 5^{2} \cdot 29$	$- 3 \cdot 5^{9} \cdot 29$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.4	5B.1.3	$870$	$48$	$1$	$11.92681209$	$1$		$0$	$4560$	$0.946019$	$-301302001664/87$	$1.19848$	$5.32433$	$[0, -1, 1, -17458, -882057]$	$y^2+y=x^3-x^2-17458x-882057$	5.24.0-5.a.2.1, 870.48.1.?	$[(1180533/82, 659971191/82)]$
2175.j2	2175f2	2175.j	2175f	$2$	$5$	$3 \cdot 5^{2} \cdot 29$	$- 3^{5} \cdot 5^{9} \cdot 29^{5}$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.2	5B.1.4	$870$	$48$	$1$	$2.385362418$	$1$		$0$	$22800$	$1.750738$	$1351431663616/4984209207$	$1.01570$	$5.73842$	$[0, -1, 1, 28792, -4368307]$	$y^2+y=x^3-x^2+28792x-4368307$	5.24.0-5.a.1.1, 870.48.1.?	$[(6493/2, 525621/2)]$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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