LMFDB - Elliptic curve search results

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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	Manin constant

Intrinsic torsion order

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Results (28 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
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	$870$	$48$	$1$	$1$	$1$		$0$	$912$	$0.141300$	$-301302001664/87$	$1.19848$	$4.06774$	$1$	$[0, 1, 1, -698, -7336]$	$y^2+y=x^3+x^2-698x-7336$	5.24.0-5.a.2.2, 870.48.1.?	$[ ]$	$1$
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	$870$	$48$	$1$	$11.92681209$	$1$		$0$	$4560$	$0.946019$	$-301302001664/87$	$1.19848$	$5.32433$	$1$	$[0, -1, 1, -17458, -882057]$	$y^2+y=x^3-x^2-17458x-882057$	5.24.0-5.a.2.1, 870.48.1.?	$[(1180533/82, 659971191/82)]$	$1$
6525.b1	6525m1	6525.b	6525m	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 29 $	$ - 3^{7} \cdot 5^{9} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$870$	$48$	$1$	$0.348944160$	$1$		$6$	$36480$	$1.495325$	$-301302001664/87$	$1.19848$	$5.40884$	$1$	$[0, 0, 1, -157125, 23972656]$	$y^2+y=x^3-157125x+23972656$	5.12.0.a.2, 15.24.0-5.a.2.2, 290.24.0.?, 870.48.1.?	$[(250, 562)]$	$1$
6525.l1	6525l1	6525.l	6525l	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 29 $	$ - 3^{7} \cdot 5^{3} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$870$	$48$	$1$	$1.007333986$	$1$		$0$	$7296$	$0.690606$	$-301302001664/87$	$1.19848$	$4.30942$	$1$	$[0, 0, 1, -6285, 191781]$	$y^2+y=x^3-6285x+191781$	5.12.0.a.2, 15.24.0-5.a.2.1, 290.24.0.?, 870.48.1.?	$[(185/2, 41/2)]$	$1$
34800.bj1	34800co1	34800.bj	34800co	$2$	$5$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 29 $	$ - 2^{12} \cdot 3 \cdot 5^{3} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1740$	$48$	$1$	$1$	$1$		$0$	$36480$	$0.834447$	$-301302001664/87$	$1.19848$	$3.78465$	$1$	$[0, -1, 0, -11173, 458317]$	$y^2=x^3-x^2-11173x+458317$	5.12.0.a.2, 20.24.0-5.a.2.2, 870.24.1.?, 1740.48.1.?	$[ ]$	$1$
34800.co1	34800dt1	34800.co	34800dt	$2$	$5$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 29 $	$ - 2^{12} \cdot 3 \cdot 5^{9} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1740$	$48$	$1$	$4.230402876$	$1$		$0$	$182400$	$1.639166$	$-301302001664/87$	$1.19848$	$4.70807$	$1$	$[0, 1, 0, -279333, 56730963]$	$y^2=x^3+x^2-279333x+56730963$	5.12.0.a.2, 20.24.0-5.a.2.1, 870.24.1.?, 1740.48.1.?	$[(14942/7, 1875/7)]$	$1$
63075.e1	63075u1	63075.e	63075u	$2$	$5$	$ 3 \cdot 5^{2} \cdot 29^{2} $	$ - 3 \cdot 5^{9} \cdot 29^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$870$	$48$	$1$	$30.30356499$	$1$		$0$	$3830400$	$2.629665$	$-301302001664/87$	$1.19848$	$5.53019$	$1$	$[0, 1, 1, -14682458, -21659305756]$	$y^2+y=x^3+x^2-14682458x-21659305756$	5.12.0.a.2, 30.24.0-5.a.2.1, 145.24.0.?, 870.48.1.?	$[(110725497832893/152014, 471595031085775067503/152014)]$	$1$
63075.w1	63075i1	63075.w	63075i	$2$	$5$	$ 3 \cdot 5^{2} \cdot 29^{2} $	$ - 3 \cdot 5^{3} \cdot 29^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$870$	$48$	$1$	$1$	$9$	$3$	$0$	$766080$	$1.824947$	$-301302001664/87$	$1.19848$	$4.65645$	$1$	$[0, -1, 1, -587298, -173039527]$	$y^2+y=x^3-x^2-587298x-173039527$	5.12.0.a.2, 30.24.0-5.a.2.2, 145.24.0.?, 870.48.1.?	$[ ]$	$1$
104400.bn1	104400fq1	104400.bn	104400fq	$2$	$5$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ - 2^{12} \cdot 3^{7} \cdot 5^{9} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1740$	$48$	$1$	$1$	$9$	$3$	$0$	$1459200$	$2.188473$	$-301302001664/87$	$1.19848$	$4.83090$	$1$	$[0, 0, 0, -2514000, -1534250000]$	$y^2=x^3-2514000x-1534250000$	5.12.0.a.2, 60.24.0-5.a.2.1, 580.24.0.?, 870.24.1.?, 1740.48.1.?	$[ ]$	$1$
104400.ep1	104400fl1	104400.ep	104400fl	$2$	$5$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ - 2^{12} \cdot 3^{7} \cdot 5^{3} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$1740$	$48$	$1$	$1$	$1$		$0$	$291840$	$1.383753$	$-301302001664/87$	$1.19848$	$3.99526$	$1$	$[0, 0, 0, -100560, -12274000]$	$y^2=x^3-100560x-12274000$	5.12.0.a.2, 60.24.0-5.a.2.2, 580.24.0.?, 870.24.1.?, 1740.48.1.?	$[ ]$	$1$
106575.b1	106575bo1	106575.b	106575bo	$2$	$5$	$ 3 \cdot 5^{2} \cdot 7^{2} \cdot 29 $	$ - 3 \cdot 5^{3} \cdot 7^{6} \cdot 29 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$6090$	$48$	$1$	$0.941143259$	$1$		$12$	$328320$	$1.114256$	$-301302001664/87$	$1.19848$	$3.70879$	$1$	$[0, -1, 1, -34218, 2447738]$	$y^2+y=x^3-x^2-34218x+2447738$	5.12.0.a.2, 35.24.0-5.a.2.2, 870.24.1.?, 6090.48.1.?	$[(103, 73), (107, 2)]$	$1$
106575.cz1	106575dc1	106575.cz	106575dc	$2$	$5$	$ 3 \cdot 5^{2} \cdot 7^{2} \cdot 29 $	$ - 3 \cdot 5^{9} \cdot 7^{6} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$6090$	$48$	$1$	$8.358199905$	$1$		$0$	$1641600$	$1.918974$	$-301302001664/87$	$1.19848$	$4.54294$	$1$	$[0, 1, 1, -855458, 304256369]$	$y^2+y=x^3+x^2-855458x+304256369$	5.12.0.a.2, 35.24.0-5.a.2.1, 870.24.1.?, 6090.48.1.?	$[(479389/30, 1101887/30)]$	$1$
139200.z1	139200cp1	139200.z	139200cp	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3 \cdot 5^{9} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$1.971893243$	$1$		$0$	$364800$	$1.292593$	$-301302001664/87$	$1.19848$	$3.80585$	$1$	$[0, -1, 0, -69833, 7126287]$	$y^2=x^3-x^2-69833x+7126287$	5.12.0.a.2, 40.24.0-5.a.2.2, 870.24.1.?, 3480.48.1.?	$[(1378/3, 125/3)]$	$1$
139200.bk1	139200hu1	139200.bk	139200hu	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3 \cdot 5^{3} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$1$	$1$		$0$	$72960$	$0.487874$	$-301302001664/87$	$1.19848$	$2.99051$	$1$	$[0, -1, 0, -2793, -55893]$	$y^2=x^3-x^2-2793x-55893$	5.12.0.a.2, 40.24.0-5.a.2.3, 870.24.1.?, 3480.48.1.?	$[ ]$	$1$
139200.im1	139200q1	139200.im	139200q	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3 \cdot 5^{3} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$1$	$1$		$0$	$72960$	$0.487874$	$-301302001664/87$	$1.19848$	$2.99051$	$1$	$[0, 1, 0, -2793, 55893]$	$y^2=x^3+x^2-2793x+55893$	5.12.0.a.2, 40.24.0-5.a.2.1, 870.24.1.?, 3480.48.1.?	$[ ]$	$1$
139200.iw1	139200fr1	139200.iw	139200fr	$2$	$5$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3 \cdot 5^{9} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$36.54986150$	$1$		$0$	$364800$	$1.292593$	$-301302001664/87$	$1.19848$	$3.80585$	$1$	$[0, 1, 0, -69833, -7126287]$	$y^2=x^3+x^2-69833x-7126287$	5.12.0.a.2, 40.24.0-5.a.2.4, 870.24.1.?, 3480.48.1.?	$[(69780165053206072/9483903, 17193279554453115970856875/9483903)]$	$1$
189225.b1	189225b1	189225.b	189225b	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 29^{2} $	$ - 3^{7} \cdot 5^{3} \cdot 29^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$870$	$48$	$1$	$0.321068882$	$1$		$6$	$6128640$	$2.374252$	$-301302001664/87$	$1.19848$	$4.77793$	$1$	$[0, 0, 1, -5285685, 4677352906]$	$y^2+y=x^3-5285685x+4677352906$	5.12.0.a.2, 10.24.0-5.a.2.1, 435.24.0.?, 870.48.1.?	$[(1015, 18922)]$	$1$
189225.br1	189225bq1	189225.br	189225bq	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 29^{2} $	$ - 3^{7} \cdot 5^{9} \cdot 29^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$870$	$48$	$1$	$5.285616094$	$1$		$0$	$30643200$	$3.178974$	$-301302001664/87$	$1.19848$	$5.57267$	$1$	$[0, 0, 1, -132142125, 584669113281]$	$y^2+y=x^3-132142125x+584669113281$	5.12.0.a.2, 10.24.0-5.a.2.2, 435.24.0.?, 870.48.1.?	$[(88769/4, 9559615/4)]$	$1$
263175.d1	263175d1	263175.d	263175d	$2$	$5$	$ 3 \cdot 5^{2} \cdot 11^{2} \cdot 29 $	$ - 3 \cdot 5^{9} \cdot 11^{6} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$9570$	$48$	$1$	$3.605413490$	$1$		$2$	$6156000$	$2.144966$	$-301302001664/87$	$1.19848$	$4.43118$	$1$	$[0, -1, 1, -2112458, 1182467318]$	$y^2+y=x^3-x^2-2112458x+1182467318$	5.12.0.a.2, 55.24.0-5.a.2.2, 870.24.1.?, 9570.48.1.?	$[(1042, 10562)]$	$1$
263175.cx1	263175cx1	263175.cx	263175cx	$2$	$5$	$ 3 \cdot 5^{2} \cdot 11^{2} \cdot 29 $	$ - 3 \cdot 5^{3} \cdot 11^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$9570$	$48$	$1$	$1$	$1$		$0$	$1231200$	$1.340248$	$-301302001664/87$	$1.19848$	$3.65745$	$1$	$[0, 1, 1, -84498, 9425939]$	$y^2+y=x^3+x^2-84498x+9425939$	5.12.0.a.2, 55.24.0-5.a.2.1, 870.24.1.?, 9570.48.1.?	$[ ]$	$1$
319725.l1	319725l1	319725.l	319725l	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 29 $	$ - 3^{7} \cdot 5^{9} \cdot 7^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$6090$	$48$	$1$	$1$	$4$	$2$	$0$	$13132800$	$2.468281$	$-301302001664/87$	$1.19848$	$4.66923$	$1$	$[0, 0, 1, -7699125, -8222621094]$	$y^2+y=x^3-7699125x-8222621094$	5.12.0.a.2, 105.24.0.?, 870.24.1.?, 2030.24.0.?, 6090.48.1.?	$[ ]$	$1$
319725.eh1	319725eh1	319725.eh	319725eh	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 29 $	$ - 3^{7} \cdot 5^{3} \cdot 7^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$6090$	$48$	$1$	$1$	$4$	$2$	$0$	$2626560$	$1.663561$	$-301302001664/87$	$1.19848$	$3.90738$	$1$	$[0, 0, 1, -307965, -65780969]$	$y^2+y=x^3-307965x-65780969$	5.12.0.a.2, 105.24.0.?, 870.24.1.?, 2030.24.0.?, 6090.48.1.?	$[ ]$	$1$
367575.a1	367575a1	367575.a	367575a	$2$	$5$	$ 3 \cdot 5^{2} \cdot 13^{2} \cdot 29 $	$ - 3 \cdot 5^{9} \cdot 13^{6} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$11310$	$48$	$1$	$8.049295875$	$1$		$0$	$9849600$	$2.228493$	$-301302001664/87$	$1.19848$	$4.39387$	$1$	$[0, -1, 1, -2950458, -1949680432]$	$y^2+y=x^3-x^2-2950458x-1949680432$	5.12.0.a.2, 65.24.0-5.a.2.2, 870.24.1.?, 11310.48.1.?	$[(439297/4, 290574343/4)]$	$1$
367575.cc1	367575cc1	367575.cc	367575cc	$2$	$5$	$ 3 \cdot 5^{2} \cdot 13^{2} \cdot 29 $	$ - 3 \cdot 5^{3} \cdot 13^{6} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$11310$	$48$	$1$	$1$	$25$	$5$	$0$	$1969920$	$1.423775$	$-301302001664/87$	$1.19848$	$3.64031$	$1$	$[0, 1, 1, -118018, -15644651]$	$y^2+y=x^3+x^2-118018x-15644651$	5.12.0.a.2, 65.24.0-5.a.2.1, 870.24.1.?, 11310.48.1.?	$[ ]$	$1$
417600.di1	417600di1	417600.di	417600di	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{3} \cdot 29 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$1.211127448$	$1$		$8$	$583680$	$1.037180$	$-301302001664/87$	$1.19848$	$3.24597$	$1$	$[0, 0, 0, -25140, 1534250]$	$y^2=x^3-25140x+1534250$	5.12.0.a.2, 120.24.0.?, 870.24.1.?, 1160.24.0.?, 3480.48.1.?	$[(91, 9), (115, 405)]$	$1$
417600.fb1	417600fb1	417600.fb	417600fb	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{9} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$14.23840547$	$1$		$0$	$2918400$	$1.841898$	$-301302001664/87$	$1.19848$	$3.99210$	$1$	$[0, 0, 0, -628500, -191781250]$	$y^2=x^3-628500x-191781250$	5.12.0.a.2, 120.24.0.?, 870.24.1.?, 1160.24.0.?, 3480.48.1.?	$[(4092631/65, 2858392971/65)]$	$1$
417600.ky1	417600ky1	417600.ky	417600ky	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{9} \cdot 29 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$1$	$1$		$0$	$2918400$	$1.841898$	$-301302001664/87$	$1.19848$	$3.99210$	$1$	$[0, 0, 0, -628500, 191781250]$	$y^2=x^3-628500x+191781250$	5.12.0.a.2, 120.24.0.?, 870.24.1.?, 1160.24.0.?, 3480.48.1.?	$[ ]$	$1$
417600.mj1	417600mj1	417600.mj	417600mj	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 $	$ - 2^{6} \cdot 3^{7} \cdot 5^{3} \cdot 29 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3480$	$48$	$1$	$11.14789129$	$1$		$0$	$583680$	$1.037180$	$-301302001664/87$	$1.19848$	$3.24597$	$1$	$[0, 0, 0, -25140, -1534250]$	$y^2=x^3-25140x-1534250$	5.12.0.a.2, 120.24.0.?, 870.24.1.?, 1160.24.0.?, 3480.48.1.?	$[(122175/19, 36758875/19)]$	$1$

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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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Results (28 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.

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