LMFDB - Elliptic curves over $\Q$ of conductor 770

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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 (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	Semistable	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
770.a1	770b4	770.a	770b	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{9} \cdot 5^{6} \cdot 7 \cdot 11^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$9240$	$96$	$1$	$1$	$1$	$0$	$3456$	$1.397518$	$423783056881319689/99207416000000$	$0.98254$	$6.10677$	$[1, 0, 1, -15649, 580116]$	$y^2+xy+y=x^3-15649x+580116$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 56.6.0.a.1, 168.48.0.?, $\ldots$	$[]$
770.a2	770b2	770.a	770b	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{3} \cdot 5^{2} \cdot 7^{3} \cdot 11^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$9240$	$96$	$1$	$1$	$1$	$4$	$1152$	$0.848212$	$346553430870203929/8300600$	$0.97551$	$6.07650$	$[1, 0, 1, -14634, 680132]$	$y^2+xy+y=x^3-14634x+680132$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 56.6.0.a.1, 168.48.0.?, $\ldots$	$[]$
770.a3	770b1	770.a	770b	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 5 \cdot 7^{6} \cdot 11 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$9240$	$96$	$1$	$1$	$1$	$5$	$576$	$0.501638$	$-84309998289049/414124480$	$0.93048$	$4.82577$	$[1, 0, 1, -914, 10596]$	$y^2+xy+y=x^3-914x+10596$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 56.6.0.d.1, 110.6.0.?, $\ldots$	$[]$
770.a4	770b3	770.a	770b	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{18} \cdot 5^{3} \cdot 7^{2} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$9240$	$96$	$1$	$1$	$1$	$1$	$1728$	$1.050945$	$1296134247276791/2137096192000$	$0.96746$	$5.32814$	$[1, 0, 1, 2271, 56852]$	$y^2+xy+y=x^3+2271x+56852$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 56.6.0.d.1, 110.6.0.?, $\ldots$	$[]$
770.b1	770d2	770.b	770d	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$308$	$12$	$0$	$0.120889825$	$1$	$18$	$512$	$0.586879$	$67324767141241/3368750000$	$0.93010$	$4.79065$	$[1, 0, 1, -848, 9006]$	$y^2+xy+y=x^3-848x+9006$	2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.?	$[(5, 67)]$
770.b2	770d1	770.b	770d	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 5^{4} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$308$	$12$	$0$	$0.241779650$	$1$	$11$	$256$	$0.240305$	$3789119879/135520000$	$0.92906$	$3.93643$	$[1, 0, 1, 32, 558]$	$y^2+xy+y=x^3+32x+558$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.?	$[(4, 25)]$
770.c1	770c3	770.c	770c	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{2} \cdot 5^{5} \cdot 7^{2} \cdot 11^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.8	2B	$440$	$48$	$0$	$1$	$1$	$0$	$10240$	$2.040012$	$3855131356812007128171561/8967612500$	$1.05520$	$8.51762$	$[1, -1, 0, -3266669, -2271693567]$	$y^2+xy=x^3-x^2-3266669x-2271693567$	2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 88.24.0.?, $\ldots$	$[]$
770.c2	770c4	770.c	770c	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{2} \cdot 5^{20} \cdot 7^{2} \cdot 11 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.7	2B	$440$	$48$	$0$	$1$	$1$	$2$	$10240$	$2.040012$	$1098325674097093229481/205612182617187500$	$1.03730$	$7.28938$	$[1, -1, 0, -214949, -31495495]$	$y^2+xy=x^3-x^2-214949x-31495495$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 44.24.0-44.h.1.2, 440.48.0.?	$[]$
770.c3	770c2	770.c	770c	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{4} \cdot 5^{10} \cdot 7^{4} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.1	2Cs	$220$	$48$	$0$	$1$	$1$	$2$	$5120$	$1.693439$	$941226862950447171561/45393906250000$	$1.05886$	$7.26616$	$[1, -1, 0, -204169, -35456067]$	$y^2+xy=x^3-x^2-204169x-35456067$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 44.24.0-44.a.1.1, 220.48.0.?	$[]$
770.c4	770c1	770.c	770c	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{8} \cdot 5^{5} \cdot 7^{8} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.6	2B	$440$	$48$	$0$	$1$	$1$	$1$	$2560$	$1.346867$	$-195395722614328041/50730248800000$	$1.03575$	$6.04605$	$[1, -1, 0, -12089, -612755]$	$y^2+xy=x^3-x^2-12089x-612755$	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, $\ldots$	$[]$
770.d1	770e3	770.d	770e	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{4} \cdot 5 \cdot 7^{2} \cdot 11^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.8	2B	$440$	$48$	$0$	$2.235814959$	$1$	$2$	$1024$	$0.955394$	$1010962818911303721/57392720$	$1.00694$	$6.23759$	$[1, -1, 0, -20909, -1158507]$	$y^2+xy=x^3-x^2-20909x-1158507$	2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 88.24.0.?, $\ldots$	$[(189, 1176)]$
770.d2	770e4	770.d	770e	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{4} \cdot 5^{4} \cdot 7^{8} \cdot 11 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.7	2B	$440$	$48$	$0$	$0.558953739$	$1$	$14$	$1024$	$0.955394$	$1160306142246441/634128110000$	$1.01881$	$5.21899$	$[1, -1, 0, -2189, 9845]$	$y^2+xy=x^3-x^2-2189x+9845$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 44.24.0-44.h.1.2, 440.48.0.?	$[(1, 87)]$
770.d3	770e2	770.d	770e	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{8} \cdot 5^{2} \cdot 7^{4} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.1	2Cs	$220$	$48$	$0$	$1.117907479$	$1$	$10$	$512$	$0.608820$	$248158561089321/1859334400$	$0.99943$	$4.98693$	$[1, -1, 0, -1309, -17787]$	$y^2+xy=x^3-x^2-1309x-17787$	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 44.24.0-44.a.1.1, 220.48.0.?	$[(-21, 0)]$
770.d4	770e1	770.d	770e	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{16} \cdot 5 \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.6	2B	$440$	$48$	$0$	$2.235814959$	$1$	$3$	$256$	$0.262247$	$-2749884201/176619520$	$1.01909$	$3.98008$	$[1, -1, 0, -29, -635]$	$y^2+xy=x^3-x^2-29x-635$	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, $\ldots$	$[(19, 64)]$
770.e1	770a2	770.e	770a	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2 \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3080$	$12$	$0$	$1$	$1$	$0$	$128$	$-0.191014$	$43949604889/42350$	$0.87006$	$3.68716$	$[1, 1, 0, -73, -273]$	$y^2+xy=x^3+x^2-73x-273$	2.3.0.a.1, 56.6.0.a.1, 220.6.0.?, 3080.12.0.?	$[]$
770.e2	770a1	770.e	770a	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3080$	$12$	$0$	$1$	$1$	$1$	$64$	$-0.537587$	$-4826809/10780$	$0.90292$	$2.55335$	$[1, 1, 0, -3, -7]$	$y^2+xy=x^3+x^2-3x-7$	2.3.0.a.1, 56.6.0.d.1, 110.6.0.?, 3080.12.0.?	$[]$
770.f1	770f4	770.f	770f	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{2} \cdot 5^{12} \cdot 7^{2} \cdot 11^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$924$	$96$	$1$	$3.124064275$	$1$	$2$	$3456$	$1.422663$	$1969902499564819009/63690429687500$	$0.98376$	$6.33795$	$[1, 0, 0, -26116, -1580604]$	$y^2+xy=x^3-26116x-1580604$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 28.6.0.c.1, 44.6.0.a.1, $\ldots$	$[(-96, 258)]$
770.f2	770f2	770.f	770f	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{6} \cdot 5^{4} \cdot 7^{6} \cdot 11 $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$924$	$96$	$1$	$1.041354758$	$1$	$16$	$1152$	$0.873356$	$5057359576472449/51765560000$	$0.95486$	$5.44049$	$[1, 0, 0, -3576, 81280]$	$y^2+xy=x^3-3576x+81280$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 28.6.0.c.1, 44.6.0.a.1, $\ldots$	$[(38, 6)]$
770.f3	770f1	770.f	770f	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 5^{2} \cdot 7^{3} \cdot 11^{2} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$924$	$96$	$1$	$0.520677379$	$1$	$23$	$576$	$0.526783$	$-19443408769/4249907200$	$0.97281$	$4.45769$	$[1, 0, 0, -56, 3136]$	$y^2+xy=x^3-56x+3136$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 14.6.0.b.1, 42.48.0-42.b.1.4, $\ldots$	$[(6, 52)]$
770.f4	770f3	770.f	770f	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 5^{6} \cdot 7 \cdot 11^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$924$	$96$	$1$	$1.562032137$	$1$	$3$	$1728$	$1.076088$	$14156681599871/3100231750000$	$1.00754$	$5.44876$	$[1, 0, 0, 504, -84560]$	$y^2+xy=x^3+504x-84560$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 14.6.0.b.1, 42.48.0-42.b.1.3, $\ldots$	$[(58, 346)]$
770.g1	770g4	770.g	770g	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2 \cdot 5^{2} \cdot 7^{3} \cdot 11^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$9240$	$96$	$1$	$1$	$1$	$0$	$1152$	$0.848818$	$4823468134087681/30382271150$	$0.95452$	$5.43337$	$[1, 0, 0, -3520, -80238]$	$y^2+xy=x^3-3520x-80238$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 56.6.0.a.1, 168.48.0.?, $\ldots$	$[]$
770.g2	770g2	770.g	770g	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{3} \cdot 5^{6} \cdot 7 \cdot 11^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$9240$	$96$	$1$	$1$	$1$	$4$	$384$	$0.299511$	$2177286259681/105875000$	$0.90546$	$4.27437$	$[1, 0, 0, -270, 1612]$	$y^2+xy=x^3-270x+1612$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 56.6.0.a.1, 168.48.0.?, $\ldots$	$[]$
770.g3	770g3	770.g	770g	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{2} \cdot 5 \cdot 7^{6} \cdot 11^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$9240$	$96$	$1$	$1$	$1$	$1$	$576$	$0.502244$	$-80677568161/3131816380$	$0.95293$	$4.41358$	$[1, 0, 0, -90, -2720]$	$y^2+xy=x^3-90x-2720$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 56.6.0.d.1, 110.6.0.?, $\ldots$	$[]$
770.g4	770g1	770.g	770g	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 5^{3} \cdot 7^{2} \cdot 11 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$9240$	$96$	$1$	$1$	$1$	$5$	$192$	$-0.047062$	$109902239/4312000$	$0.89937$	$3.41791$	$[1, 0, 0, 10, 100]$	$y^2+xy=x^3+10x+100$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 56.6.0.d.1, 110.6.0.?, $\ldots$	$[]$

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

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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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