LMFDB - Elliptic curves over $\Q$ of conductor 1575

Refine search

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	Manin constant

		Sort order	Select

Results (29 matches)

Download displayed columns for results to

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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1575.a1	1575i2	1575.a	1575i	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{6} \cdot 5^{9} \cdot 7^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$210$	$48$	$1$	$4.245874128$	$1$	$2$	$6000$	$1.408218$	$-2887553024/16807$	$0.98803$	$5.82318$	$[0, 0, 1, -33375, -2358594]$	$y^2+y=x^3-33375x-2358594$	5.12.0.a.1, 15.24.0-5.a.1.2, 70.24.1.d.1, 210.48.1.?	$[(675, 16812)]$
1575.a2	1575i1	1575.a	1575i	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{6} \cdot 5^{9} \cdot 7 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$210$	$48$	$1$	$0.849174825$	$1$	$4$	$1200$	$0.603499$	$4096/7$	$0.98030$	$4.08364$	$[0, 0, 1, 375, 3906]$	$y^2+y=x^3+375x+3906$	5.12.0.a.2, 15.24.0-5.a.2.2, 70.24.1.d.2, 210.48.1.?	$[(0, 62)]$
1575.b1	1575b2	1575.b	1575b	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{9} \cdot 5^{9} \cdot 7^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.29	2B	$1680$	$96$	$3$	$1$	$1$	$0$	$3840$	$1.387657$	$8869743/2401$	$0.92625$	$5.48364$	$[1, -1, 1, -14555, -489428]$	$y^2+xy+y=x^3-x^2-14555x-489428$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.s.1, 48.24.0.l.2, 56.24.0.dm.1, $\ldots$	$[ ]$
1575.b2	1575b1	1575.b	1575b	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{9} \cdot 5^{9} \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.31	2B	$1680$	$96$	$3$	$1$	$1$	$1$	$1920$	$1.041084$	$35937/49$	$0.83942$	$4.77677$	$[1, -1, 1, 2320, -50678]$	$y^2+xy+y=x^3-x^2+2320x-50678$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.v.1, 28.12.0.n.1, 30.6.0.a.1, $\ldots$	$[ ]$
1575.c1	1575g5	1575.c	1575g	$6$	$8$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{7} \cdot 5^{6} \cdot 7^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$1680$	$192$	$1$	$0.945149794$	$1$	$4$	$4096$	$1.428230$	$53297461115137/147$	$1.05087$	$6.50029$	$[1, -1, 1, -176405, 28561722]$	$y^2+xy+y=x^3-x^2-176405x+28561722$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$	$[(243, -115)]$
1575.c2	1575g4	1575.c	1575g	$6$	$8$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{8} \cdot 5^{6} \cdot 7^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.18	2Cs	$840$	$192$	$1$	$0.472574897$	$1$	$16$	$2048$	$1.081657$	$13027640977/21609$	$1.08149$	$5.37063$	$[1, -1, 1, -11030, 447972]$	$y^2+xy+y=x^3-x^2-11030x+447972$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 20.24.0-4.b.1.2, $\ldots$	$[(68, 60)]$
1575.c3	1575g3	1575.c	1575g	$6$	$8$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{14} \cdot 5^{6} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.88	2B	$1680$	$192$	$1$	$1.890299589$	$1$	$4$	$2048$	$1.081657$	$6570725617/45927$	$1.00160$	$5.27766$	$[1, -1, 1, -8780, -312528]$	$y^2+xy+y=x^3-x^2-8780x-312528$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$	$[(-51, 0)]$
1575.c4	1575g6	1575.c	1575g	$6$	$8$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{7} \cdot 5^{6} \cdot 7^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.90	2B	$1680$	$192$	$1$	$0.236287448$	$1$	$12$	$4096$	$1.428230$	$-4354703137/17294403$	$1.04266$	$5.50189$	$[1, -1, 1, -7655, 724722]$	$y^2+xy+y=x^3-x^2-7655x+724722$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[(14, 780)]$
1575.c5	1575g2	1575.c	1575g	$6$	$8$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{10} \cdot 5^{6} \cdot 7^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.10	2Cs	$840$	$192$	$1$	$0.945149794$	$1$	$12$	$1024$	$0.735084$	$7189057/3969$	$1.14862$	$4.35158$	$[1, -1, 1, -905, 2472]$	$y^2+xy+y=x^3-x^2-905x+2472$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$	$[(-6, 90)]$
1575.c6	1575g1	1575.c	1575g	$6$	$8$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{8} \cdot 5^{6} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.1	2B	$1680$	$192$	$1$	$1.890299589$	$1$	$5$	$512$	$0.388510$	$103823/63$	$0.97868$	$3.77597$	$[1, -1, 1, 220, 222]$	$y^2+xy+y=x^3-x^2+220x+222$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$	$[(8, 45)]$
1575.d1	1575d2	1575.d	1575d	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{3} \cdot 5^{3} \cdot 7^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.29	2B	$1680$	$96$	$3$	$0.215604345$	$1$	$10$	$256$	$0.033633$	$8869743/2401$	$0.92625$	$3.27659$	$[1, -1, 1, -65, 162]$	$y^2+xy+y=x^3-x^2-65x+162$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.s.1, 48.24.0.l.2, 56.24.0.dm.1, $\ldots$	$[(8, 6)]$
1575.d2	1575d1	1575.d	1575d	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{3} \cdot 5^{3} \cdot 7^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.31	2B	$1680$	$96$	$3$	$0.431208691$	$1$	$9$	$128$	$-0.312941$	$35937/49$	$0.83942$	$2.56972$	$[1, -1, 1, 10, 12]$	$y^2+xy+y=x^3-x^2+10x+12$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.v.1, 28.12.0.n.1, 30.6.0.a.1, $\ldots$	$[(0, 3)]$
1575.e1	1575j1	1575.e	1575j	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{9} \cdot 5^{9} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$420$	$12$	$0$	$1$	$1$	$1$	$1920$	$0.962808$	$5177717/189$	$0.97949$	$4.96284$	$[1, -1, 1, -4055, -95178]$	$y^2+xy+y=x^3-x^2-4055x-95178$	2.3.0.a.1, 20.6.0.b.1, 84.6.0.?, 210.6.0.?, 420.12.0.?	$[ ]$
1575.e2	1575j2	1575.e	1575j	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{12} \cdot 5^{9} \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$420$	$12$	$0$	$1$	$1$	$0$	$3840$	$1.309381$	$300763/35721$	$1.11388$	$5.29882$	$[1, -1, 1, 1570, -342678]$	$y^2+xy+y=x^3-x^2+1570x-342678$	2.3.0.a.1, 20.6.0.a.1, 84.6.0.?, 420.12.0.?	$[ ]$
1575.f1	1575e3	1575.f	1575e	$3$	$9$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{6} \cdot 5^{15} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$630$	$144$	$3$	$1$	$1$	$0$	$4320$	$1.481487$	$-250523582464/13671875$	$1.02112$	$5.78446$	$[0, 0, 1, -29550, 2045281]$	$y^2+y=x^3-29550x+2045281$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.2, 42.8.0-3.a.1.2, 45.24.0-9.a.1.1, $\ldots$	$[ ]$
1575.f2	1575e1	1575.f	1575e	$3$	$9$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{6} \cdot 5^{7} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$630$	$144$	$3$	$1$	$1$	$0$	$480$	$0.382875$	$-262144/35$	$0.88715$	$3.92998$	$[0, 0, 1, -300, -2219]$	$y^2+y=x^3-300x-2219$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.1, 42.8.0-3.a.1.1, 45.24.0-9.a.1.2, $\ldots$	$[ ]$
1575.f3	1575e2	1575.f	1575e	$3$	$9$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{6} \cdot 5^{9} \cdot 7^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$630$	$144$	$3$	$1$	$1$	$0$	$1440$	$0.932181$	$71991296/42875$	$1.06493$	$4.66454$	$[0, 0, 1, 1950, 5656]$	$y^2+y=x^3+1950x+5656$	3.12.0.a.1, 15.24.0-3.a.1.1, 42.24.0-3.a.1.1, 63.36.0.b.1, 70.2.0.a.1, $\ldots$	$[ ]$
1575.g1	1575a2	1575.g	1575a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{3} \cdot 5^{9} \cdot 7^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.29	2B	$1680$	$96$	$3$	$1$	$1$	$0$	$1280$	$0.838351$	$8869743/2401$	$0.92625$	$4.58828$	$[1, -1, 0, -1617, 18666]$	$y^2+xy=x^3-x^2-1617x+18666$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.s.1, 48.24.0.l.2, 56.24.0.dm.1, $\ldots$	$[ ]$
1575.g2	1575a1	1575.g	1575a	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{3} \cdot 5^{9} \cdot 7^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.31	2B	$1680$	$96$	$3$	$1$	$1$	$1$	$640$	$0.491778$	$35937/49$	$0.83942$	$3.88140$	$[1, -1, 0, 258, 1791]$	$y^2+xy=x^3-x^2+258x+1791$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.v.1, 28.12.0.n.1, 30.6.0.a.1, $\ldots$	$[ ]$
1575.h1	1575f3	1575.h	1575f	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{7} \cdot 5^{10} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$1$	$0$	$3072$	$1.188063$	$157551496201/13125$	$0.96087$	$5.70922$	$[1, -1, 0, -25317, 1556716]$	$y^2+xy=x^3-x^2-25317x+1556716$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.ba.1, 42.6.0.a.1, $\ldots$	$[ ]$
1575.h2	1575f2	1575.h	1575f	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{8} \cdot 5^{8} \cdot 7^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$420$	$48$	$0$	$1$	$1$	$2$	$1536$	$0.841490$	$47045881/11025$	$1.04751$	$4.60675$	$[1, -1, 0, -1692, 21091]$	$y^2+xy=x^3-x^2-1692x+21091$	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.a.1, 28.12.0-2.a.1.2, 60.24.0-20.a.1.2, $\ldots$	$[ ]$
1575.h3	1575f1	1575.h	1575f	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{7} \cdot 5^{7} \cdot 7 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$1$	$1$	$768$	$0.494916$	$1771561/105$	$0.96659$	$4.16132$	$[1, -1, 0, -567, -4784]$	$y^2+xy=x^3-x^2-567x-4784$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.ba.1, 56.12.0-4.c.1.3, $\ldots$	$[ ]$
1575.h4	1575f4	1575.h	1575f	$4$	$4$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{10} \cdot 5^{7} \cdot 7^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$840$	$48$	$0$	$1$	$1$	$0$	$3072$	$1.188063$	$590589719/972405$	$0.94478$	$5.03361$	$[1, -1, 0, 3933, 127966]$	$y^2+xy=x^3-x^2+3933x+127966$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 20.12.0.h.1, 56.12.0-4.c.1.3, $\ldots$	$[ ]$
1575.i1	1575h1	1575.i	1575h	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{9} \cdot 5^{3} \cdot 7 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$420$	$12$	$0$	$2.513802022$	$1$	$3$	$384$	$0.158088$	$5177717/189$	$0.97949$	$3.65116$	$[1, -1, 0, -162, -729]$	$y^2+xy=x^3-x^2-162x-729$	2.3.0.a.1, 20.6.0.b.1, 84.6.0.?, 210.6.0.?, 420.12.0.?	$[(30, 129)]$
1575.i2	1575h2	1575.i	1575h	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{12} \cdot 5^{3} \cdot 7^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$420$	$12$	$0$	$1.256901011$	$1$	$4$	$768$	$0.504663$	$300763/35721$	$1.11388$	$3.98713$	$[1, -1, 0, 63, -2754]$	$y^2+xy=x^3-x^2+63x-2754$	2.3.0.a.1, 20.6.0.a.1, 84.6.0.?, 420.12.0.?	$[(18, 54)]$
1575.j1	1575c2	1575.j	1575c	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ 3^{9} \cdot 5^{3} \cdot 7^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.29	2B	$1680$	$96$	$3$	$0.860136541$	$1$	$6$	$768$	$0.582939$	$8869743/2401$	$0.92625$	$4.17196$	$[1, -1, 0, -582, -3799]$	$y^2+xy=x^3-x^2-582x-3799$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.s.1, 48.24.0.l.2, 56.24.0.dm.1, $\ldots$	$[(-16, 43)]$
1575.j2	1575c1	1575.j	1575c	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{9} \cdot 5^{3} \cdot 7^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.31	2B	$1680$	$96$	$3$	$1.720273082$	$1$	$3$	$384$	$0.236365$	$35937/49$	$0.83942$	$3.46508$	$[1, -1, 0, 93, -424]$	$y^2+xy=x^3-x^2+93x-424$	2.3.0.a.1, 4.6.0.e.1, 8.12.0.v.1, 28.12.0.n.1, 30.6.0.a.1, $\ldots$	$[(8, 24)]$
1575.k1	1575k2	1575.k	1575k	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{6} \cdot 5^{3} \cdot 7^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$210$	$48$	$1$	$1$	$1$	$0$	$1200$	$0.603499$	$-2887553024/16807$	$0.98803$	$4.51149$	$[0, 0, 1, -1335, -18869]$	$y^2+y=x^3-1335x-18869$	5.12.0.a.1, 15.24.0-5.a.1.1, 70.24.1.d.1, 210.48.1.?	$[ ]$
1575.k2	1575k1	1575.k	1575k	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 7 $	$ - 3^{6} \cdot 5^{3} \cdot 7 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$210$	$48$	$1$	$1$	$1$	$0$	$240$	$-0.201220$	$4096/7$	$0.98030$	$2.77196$	$[0, 0, 1, 15, 31]$	$y^2+y=x^3+15x+31$	5.12.0.a.2, 15.24.0-5.a.2.1, 70.24.1.d.2, 210.48.1.?	$[ ]$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (29 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Learn more

Refine search Advanced search options

Results (29 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search