LMFDB - Elliptic curves over $\Q$ of conductor 550

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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 (24 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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod- $m$ images	MW-generators
550.a1	550d2	550.a	550d	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2^{3} \cdot 5^{8} \cdot 11^{3}$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$264$	$16$	$0$	$1$	$1$	$0$	$540$	$0.568795$	$-53969305/10648$	$0.89387$	$4.90859$	$[1, 0, 1, -576, -6202]$	$y^2+xy+y=x^3-576x-6202$	3.8.0-3.a.1.1, 88.2.0.?, 264.16.0.?	$[]$
550.a2	550d1	550.a	550d	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2 \cdot 5^{8} \cdot 11$	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$264$	$16$	$0$	$1$	$1$	$2$	$180$	$0.019489$	$34295/22$	$0.82040$	$3.69549$	$[1, 0, 1, 49, 48]$	$y^2+xy+y=x^3+49x+48$	3.8.0-3.a.1.2, 88.2.0.?, 264.16.0.?	$[]$
550.b1	550c1	550.b	550c	$1$	$1$	$2 \cdot 5^{2} \cdot 11$	$- 2^{11} \cdot 5^{2} \cdot 11$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$88$	$2$	$0$	$1$	$1$	$0$	$132$	$0.048433$	$-38401771585/22528$	$0.95307$	$4.37268$	$[1, 0, 1, -206, -1152]$	$y^2+xy+y=x^3-206x-1152$	88.2.0.?	$[]$
550.c1	550g2	550.c	550g	$2$	$2$	$2 \cdot 5^{2} \cdot 11$	$2^{2} \cdot 5^{3} \cdot 11^{2}$	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.174018903$	$1$	$14$	$96$	$-0.126250$	$1039509197/484$	$0.93121$	$4.05557$	$[1, 0, 1, -106, 408]$	$y^2+xy+y=x^3-106x+408$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.d.1, 220.12.0.?	$[(3, 9)]$
550.c2	550g1	550.c	550g	$2$	$2$	$2 \cdot 5^{2} \cdot 11$	$- 2^{4} \cdot 5^{3} \cdot 11$	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$0.348037806$	$1$	$9$	$48$	$-0.472824$	$-148877/176$	$0.84151$	$2.82919$	$[1, 0, 1, -6, 8]$	$y^2+xy+y=x^3-6x+8$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.d.1, 110.6.0.?, 220.12.0.?	$[(1, 1)]$
550.d1	550a1	550.d	550a	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2^{3} \cdot 5^{7} \cdot 11$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.165868134$	$1$	$6$	$96$	$-0.002387$	$-117649/440$	$0.93815$	$3.69925$	$[1, 1, 0, -25, 125]$	$y^2+xy=x^3+x^2-25x+125$	3.4.0.a.1, 15.8.0-3.a.1.2, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(5, 10)]$
550.d2	550a2	550.d	550a	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2 \cdot 5^{9} \cdot 11^{3}$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.497604403$	$1$	$4$	$288$	$0.546920$	$80062991/332750$	$0.92204$	$4.70316$	$[1, 1, 0, 225, -3125]$	$y^2+xy=x^3+x^2+225x-3125$	3.4.0.a.1, 15.8.0-3.a.1.1, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(15, 55)]$
550.e1	550f3	550.e	550f	$3$	$25$	$2 \cdot 5^{2} \cdot 11$	$- 2^{25} \cdot 5^{9} \cdot 11$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.2	5B.1.4	$2200$	$1200$	$37$	$1.796003113$	$1$	$4$	$6000$	$1.987846$	$-24680042791780949/369098752$	$1.03557$	$8.27740$	$[1, 0, 1, -758201, 254051548]$	$y^2+xy+y=x^3-758201x+254051548$	5.24.0-5.a.1.1, 25.120.0-25.a.1.1, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[(502, -189)]$
550.e2	550f1	550.e	550f	$3$	$25$	$2 \cdot 5^{2} \cdot 11$	$- 2 \cdot 5^{9} \cdot 11$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.4	5B.1.3	$2200$	$1200$	$37$	$1.796003113$	$1$	$2$	$240$	$0.378409$	$-19465109/22$	$1.06489$	$4.95585$	$[1, 0, 1, -701, -7202]$	$y^2+xy+y=x^3-701x-7202$	5.24.0-5.a.2.1, 25.120.0-25.a.2.1, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[(52, 286)]$
550.e3	550f2	550.e	550f	$3$	$25$	$2 \cdot 5^{2} \cdot 11$	$- 2^{5} \cdot 5^{9} \cdot 11^{5}$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.120.0.2	5Cs.1.3	$2200$	$1200$	$37$	$0.359200622$	$1$	$6$	$1200$	$1.183128$	$6761990971/5153632$	$1.05709$	$5.88273$	$[1, 0, 1, 4924, 75298]$	$y^2+xy+y=x^3+4924x+75298$	5.120.0-5.a.1.1, 275.600.12.?, 440.240.5.?, 2200.1200.37.?	$[(52, 661)]$
550.f1	550b2	550.f	550b	$2$	$5$	$2 \cdot 5^{2} \cdot 11$	$- 2 \cdot 5^{7} \cdot 11^{5}$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.4	5B.1.3	$440$	$48$	$1$	$1$	$1$	$0$	$2400$	$1.449795$	$-23178622194826561/1610510$	$1.01294$	$7.50226$	$[1, 0, 1, -148501, -22038602]$	$y^2+xy+y=x^3-148501x-22038602$	5.24.0-5.a.2.1, 440.48.1.?	$[]$
550.f2	550b1	550.f	550b	$2$	$5$	$2 \cdot 5^{2} \cdot 11$	$- 2^{5} \cdot 5^{11} \cdot 11$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.24.0.2	5B.1.4	$440$	$48$	$1$	$1$	$1$	$0$	$480$	$0.645076$	$109902239/1100000$	$0.94438$	$4.90697$	$[1, 0, 1, 249, -6102]$	$y^2+xy+y=x^3+249x-6102$	5.24.0-5.a.1.1, 440.48.1.?	$[]$
550.g1	550e1	550.g	550e	$1$	$1$	$2 \cdot 5^{2} \cdot 11$	$- 2^{11} \cdot 5^{9} \cdot 11$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$1$	$1$	$0$	$880$	$0.725106$	$-2803221/22528$	$0.99503$	$5.07641$	$[1, -1, 0, -367, 10541]$	$y^2+xy=x^3-x^2-367x+10541$	440.2.0.?	$[]$
550.h1	550j1	550.h	550j	$1$	$1$	$2 \cdot 5^{2} \cdot 11$	$- 2^{11} \cdot 5^{3} \cdot 11$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$440$	$2$	$0$	$0.039906259$	$1$	$14$	$176$	$-0.079613$	$-2803221/22528$	$0.99503$	$3.54602$	$[1, -1, 1, -15, 87]$	$y^2+xy+y=x^3-x^2-15x+87$	440.2.0.?	$[(-1, 10)]$
550.i1	550i1	550.i	550i	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2^{7} \cdot 5^{7} \cdot 11^{3}$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.021400148$	$1$	$18$	$672$	$0.757527$	$-76711450249/851840$	$0.93960$	$5.50545$	$[1, 1, 1, -2213, 39531]$	$y^2+xy+y=x^3+x^2-2213x+39531$	3.4.0.a.1, 15.8.0-3.a.1.2, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(-35, 292)]$
550.i2	550i2	550.i	550i	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2^{21} \cdot 5^{9} \cdot 11$	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$0.064200444$	$1$	$12$	$2016$	$1.306833$	$2882081488391/2883584000$	$0.98944$	$6.07712$	$[1, 1, 1, 7412, 212781]$	$y^2+xy+y=x^3+x^2+7412x+212781$	3.4.0.a.1, 15.8.0-3.a.1.1, 264.8.0.?, 440.2.0.?, 1320.16.0.?	$[(5, 497)]$
550.j1	550k3	550.j	550k	$3$	$25$	$2 \cdot 5^{2} \cdot 11$	$- 2^{25} \cdot 5^{3} \cdot 11$	$0$	$\Z/5\Z$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.1	5B.1.1	$2200$	$1200$	$37$	$1$	$1$	$4$	$1200$	$1.183128$	$-24680042791780949/369098752$	$1.03557$	$6.74701$	$[1, 1, 1, -30328, 2020281]$	$y^2+xy+y=x^3+x^2-30328x+2020281$	5.24.0-5.a.1.2, 25.120.0-25.a.1.2, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[]$
550.j2	550k1	550.j	550k	$3$	$25$	$2 \cdot 5^{2} \cdot 11$	$- 2 \cdot 5^{3} \cdot 11$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	25.120.0.3	5B.1.2	$2200$	$1200$	$37$	$1$	$1$	$0$	$48$	$-0.426310$	$-19465109/22$	$1.06489$	$3.42546$	$[1, 1, 1, -28, -69]$	$y^2+xy+y=x^3+x^2-28x-69$	5.24.0-5.a.2.2, 25.120.0-25.a.2.2, 275.600.12.?, 440.48.1.?, 2200.1200.37.?	$[]$
550.j3	550k2	550.j	550k	$3$	$25$	$2 \cdot 5^{2} \cdot 11$	$- 2^{5} \cdot 5^{3} \cdot 11^{5}$	$0$	$\Z/5\Z$	$\Q$	$\mathrm{SU}(2)$	$5$	5.120.0.1	5Cs.1.1	$2200$	$1200$	$37$	$1$	$1$	$4$	$240$	$0.378409$	$6761990971/5153632$	$1.05709$	$4.35234$	$[1, 1, 1, 197, 681]$	$y^2+xy+y=x^3+x^2+197x+681$	5.120.0-5.a.1.2, 275.600.12.?, 440.240.5.?, 2200.1200.37.?	$[]$
550.k1	550l2	550.k	550l	$2$	$2$	$2 \cdot 5^{2} \cdot 11$	$2^{2} \cdot 5^{9} \cdot 11^{2}$	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$0$	$480$	$0.678469$	$1039509197/484$	$0.93121$	$5.58596$	$[1, 1, 1, -2638, 51031]$	$y^2+xy+y=x^3+x^2-2638x+51031$	2.3.0.a.1, 10.6.0.a.1, 44.6.0.d.1, 220.12.0.?	$[]$
550.k2	550l1	550.k	550l	$2$	$2$	$2 \cdot 5^{2} \cdot 11$	$- 2^{4} \cdot 5^{9} \cdot 11$	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$220$	$12$	$0$	$1$	$1$	$1$	$240$	$0.331895$	$-148877/176$	$0.84151$	$4.35958$	$[1, 1, 1, -138, 1031]$	$y^2+xy+y=x^3+x^2-138x+1031$	2.3.0.a.1, 20.6.0.c.1, 44.6.0.d.1, 110.6.0.?, 220.12.0.?	$[]$
550.l1	550m1	550.l	550m	$1$	$1$	$2 \cdot 5^{2} \cdot 11$	$- 2^{11} \cdot 5^{8} \cdot 11$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$88$	$2$	$0$	$1$	$1$	$0$	$660$	$0.853152$	$-38401771585/22528$	$0.95307$	$5.90307$	$[1, 1, 1, -5138, -143969]$	$y^2+xy+y=x^3+x^2-5138x-143969$	88.2.0.?	$[]$
550.m1	550h2	550.m	550h	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2^{3} \cdot 5^{2} \cdot 11^{3}$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$1$	$1$	$0$	$108$	$-0.235924$	$-53969305/10648$	$0.89387$	$3.37820$	$[1, 1, 1, -23, -59]$	$y^2+xy+y=x^3+x^2-23x-59$	3.4.0.a.1, 15.8.0-3.a.1.1, 88.2.0.?, 264.8.0.?, 1320.16.0.?	$[]$
550.m2	550h1	550.m	550h	$2$	$3$	$2 \cdot 5^{2} \cdot 11$	$- 2 \cdot 5^{2} \cdot 11$	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1320$	$16$	$0$	$1$	$1$	$0$	$36$	$-0.785230$	$34295/22$	$0.82040$	$2.16510$	$[1, 1, 1, 2, 1]$	$y^2+xy+y=x^3+x^2+2x+1$	3.4.0.a.1, 15.8.0-3.a.1.2, 88.2.0.?, 264.8.0.?, 1320.16.0.?	$[]$

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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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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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