LMFDB - Elliptic curves over $\Q$ of conductor 910

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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 (29 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
910.a1	910c4	910.a	910c	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{3} \cdot 5^{6} \cdot 7^{3} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$10920$	$96$	$1$	$1.012468124$	$1$		$6$	$1728$	$1.010717$	$349046010201856969/7245875000$	$0.97162$	$5.92857$	$[1, 0, 1, -14669, -685008]$	$y^2+xy+y=x^3-14669x-685008$	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.?, $\ldots$	$[(-70, 38)]$
910.a2	910c3	910.a	910c	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{6} \cdot 5^{3} \cdot 7^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$10920$	$96$	$1$	$0.506234062$	$1$		$11$	$864$	$0.664145$	$94376601570889/12235496000$	$0.93000$	$4.72277$	$[1, 0, 1, -949, -9984]$	$y^2+xy+y=x^3-949x-9984$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 56.6.0.d.1, 130.6.0.?, $\ldots$	$[(-21, 38)]$
910.a3	910c2	910.a	910c	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2 \cdot 5^{2} \cdot 7 \cdot 13^{6} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$10920$	$96$	$1$	$3.037404373$	$1$		$8$	$576$	$0.461412$	$3092354182009/1689383150$	$0.94489$	$4.22106$	$[1, 0, 1, -304, 456]$	$y^2+xy+y=x^3-304x+456$	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.?, $\ldots$	$[(-6, 48)]$
910.a4	910c1	910.a	910c	$4$	$6$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 13^{3} $	$1$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$10920$	$96$	$1$	$1.518702186$	$1$		$11$	$288$	$0.114838$	$1408317602329/2153060$	$0.89595$	$4.10562$	$[1, 0, 1, -234, 1352]$	$y^2+xy+y=x^3-234x+1352$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 56.6.0.d.1, 130.6.0.?, $\ldots$	$[(8, -1)]$
910.b1	910a3	910.b	910a	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{5} \cdot 5^{12} \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.7	2B	$520$	$48$	$0$	$1$	$4$	$2$	$0$	$3840$	$1.526964$	$143378317900125424089/4976562500000$	$1.02185$	$6.81183$	$[1, -1, 0, -109040, -13831200]$	$y^2+xy=x^3-x^2-109040x-13831200$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 40.24.0-40.y.1.6, 52.12.0-4.c.1.1, $\ldots$	$[]$
910.b2	910a2	910.b	910a	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{10} \cdot 5^{6} \cdot 7^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.1	2Cs	$520$	$48$	$0$	$1$	$1$		$2$	$1920$	$1.180391$	$39920686684059609/6492304000000$	$1.02407$	$5.61033$	$[1, -1, 0, -7120, -194304]$	$y^2+xy=x^3-x^2-7120x-194304$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.3, 52.12.0-2.a.1.1, $\ldots$	$[]$
910.b3	910a1	910.b	910a	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{20} \cdot 5^{3} \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.12	2B	$520$	$48$	$0$	$1$	$1$		$1$	$960$	$0.833817$	$884984855328729/83492864000$	$0.96922$	$5.05128$	$[1, -1, 0, -2000, 32000]$	$y^2+xy=x^3-x^2-2000x+32000$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.2, 40.24.0-40.y.1.9, $\ldots$	$[]$
910.b4	910a4	910.b	910a	$4$	$4$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{5} \cdot 5^{3} \cdot 7^{8} \cdot 13^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.8	2B	$520$	$48$	$0$	$1$	$1$		$0$	$3840$	$1.526964$	$236293804275620391/658593925444000$	$1.05092$	$6.06787$	$[1, -1, 0, 12880, -1102304]$	$y^2+xy=x^3-x^2+12880x-1102304$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.1, 40.24.0-40.s.1.4, $\ldots$	$[]$
910.c1	910d1	910.c	910d	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{2} \cdot 5^{3} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.302242933$	$1$		$9$	$96$	$-0.212176$	$2749884201/318500$	$0.95435$	$3.18999$	$[1, -1, 0, -29, -47]$	$y^2+xy=x^3-x^2-29x-47$	2.3.0.a.1, 56.6.0.c.1, 130.6.0.?, 3640.12.0.?	$[(-3, 4)]$
910.c2	910d2	910.c	910d	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2 \cdot 5^{6} \cdot 7 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.604485867$	$1$		$6$	$192$	$0.134398$	$7518017079/36968750$	$1.01440$	$3.63327$	$[1, -1, 0, 41, -285]$	$y^2+xy=x^3-x^2+41x-285$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(11, 32)]$
910.d1	910b2	910.d	910b	$2$	$3$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{3} \cdot 5^{6} \cdot 7^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.2	3B.1.2	$2184$	$16$	$0$	$0.465654782$	$1$		$4$	$432$	$0.358861$	$-22164361129/557375000$	$1.07496$	$4.05320$	$[1, 0, 1, -59, -1154]$	$y^2+xy+y=x^3-59x-1154$	3.8.0-3.a.1.1, 728.2.0.?, 2184.16.0.?	$[(58, 408)]$
910.d2	910b1	910.d	910b	$2$	$3$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2 \cdot 5^{2} \cdot 7 \cdot 13^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.8.0.1	3B.1.1	$2184$	$16$	$0$	$1.396964348$	$1$		$4$	$144$	$-0.190445$	$30080231/768950$	$0.87009$	$3.07988$	$[1, 0, 1, 6, 42]$	$y^2+xy+y=x^3+6x+42$	3.8.0-3.a.1.2, 728.2.0.?, 2184.16.0.?	$[(6, 14)]$
910.e1	910e3	910.e	910e	$3$	$9$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{63} \cdot 5^{2} \cdot 7^{3} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	9.24.0.3	3B.1.2	$6552$	$144$	$3$	$1$	$9$	$3$	$0$	$190512$	$3.357147$	$-14245586655234650511684983641/1028175397808386133196800$	$1.04760$	$9.53171$	$[1, 0, 1, -50503198, -146507820272]$	$y^2+xy+y=x^3-50503198x-146507820272$	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 117.72.0.?, 728.2.0.?, 2184.16.0.?, $\ldots$	$[]$
910.e2	910e1	910.e	910e	$3$	$9$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{7} \cdot 5^{18} \cdot 7^{3} \cdot 13 $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	9.24.0.1	3B.1.1	$6552$	$144$	$3$	$1$	$1$		$2$	$21168$	$2.258537$	$-21405018343206000779641/2177246093750000000$	$1.01453$	$7.57030$	$[1, 0, 1, -578448, 183565278]$	$y^2+xy+y=x^3-578448x+183565278$	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 117.72.0.?, 728.2.0.?, 2184.16.0.?, $\ldots$	$[]$
910.e3	910e2	910.e	910e	$3$	$9$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{21} \cdot 5^{6} \cdot 7^{9} \cdot 13^{3} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.24.0.1	3Cs.1.1	$6552$	$144$	$3$	$1$	$1$		$2$	$63504$	$2.807842$	$4998853083179567995470359/2905108466204672000000$	$1.08184$	$8.34692$	$[1, 0, 1, 3562177, -168122222]$	$y^2+xy+y=x^3+3562177x-168122222$	3.24.0-3.a.1.1, 117.72.0.?, 728.2.0.?, 2184.48.1.?, 6552.144.3.?	$[]$
910.f1	910g1	910.f	910g	$1$	$1$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{5} \cdot 5^{2} \cdot 7 \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$728$	$2$	$0$	$0.062952785$	$1$		$10$	$240$	$-0.272331$	$-3862503009/72800$	$0.85780$	$3.24456$	$[1, -1, 1, -33, 81]$	$y^2+xy+y=x^3-x^2-33x+81$	728.2.0.?	$[(5, 2)]$
910.g1	910j6	910.g	910j	$6$	$18$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2 \cdot 5^{18} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 9.24.0.3	2B, 3B.1.2	$32760$	$864$	$21$	$1$	$9$	$3$	$0$	$10368$	$2.009544$	$16375858190544687071329/9025573730468750$	$1.01214$	$7.50723$	$[1, 0, 0, -529046, -148084874]$	$y^2+xy=x^3-529046x-148084874$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 9.24.0-9.a.1.1, 18.72.0-18.a.1.2, $\ldots$	$[]$
910.g2	910j5	910.g	910j	$6$	$18$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{2} \cdot 5^{9} \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 9.24.0.3	2B, 3B.1.2	$32760$	$864$	$21$	$1$	$9$	$3$	$1$	$5184$	$1.662971$	$16369358802802724130049/4976562500$	$1.01213$	$7.50717$	$[1, 0, 0, -528976, -148126020]$	$y^2+xy=x^3-528976x-148126020$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 9.24.0-9.a.1.1, 18.72.0-18.a.1.2, $\ldots$	$[]$
910.g3	910j4	910.g	910j	$6$	$18$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{3} \cdot 5^{6} \cdot 7^{3} \cdot 13^{6} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.24.0.1	2B, 3Cs.1.1	$32760$	$864$	$21$	$1$	$1$		$4$	$3456$	$1.460239$	$932829715460155969/206949435875000$	$0.98163$	$6.07285$	$[1, 0, 0, -20356, 876120]$	$y^2+xy=x^3-20356x+876120$	2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 56.6.0.a.1, 168.144.1.?, $\ldots$	$[]$
910.g4	910j2	910.g	910j	$6$	$18$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{9} \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 9.24.0.1	2B, 3B.1.1	$32760$	$864$	$21$	$1$	$1$		$4$	$1152$	$0.910933$	$772531501373731009/15142400$	$0.97520$	$6.04517$	$[1, 0, 0, -19116, 1015696]$	$y^2+xy=x^3-19116x+1015696$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 9.24.0-9.a.1.2, 18.72.0-18.a.1.1, $\ldots$	$[]$
910.g5	910j3	910.g	910j	$6$	$18$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{6} \cdot 5^{3} \cdot 7^{6} \cdot 13^{3} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.24.0.1	2B, 3Cs.1.1	$32760$	$864$	$21$	$1$	$1$		$5$	$1728$	$1.113667$	$32318182904349889/2067798824000$	$0.96161$	$5.57932$	$[1, 0, 0, -6636, -196784]$	$y^2+xy=x^3-6636x-196784$	2.3.0.a.1, 3.24.0-3.a.1.1, 6.72.0-6.a.1.1, 56.6.0.d.1, 130.6.0.?, $\ldots$	$[]$
910.g6	910j1	910.g	910j	$6$	$18$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{18} \cdot 5 \cdot 7^{2} \cdot 13 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 9.24.0.1	2B, 3B.1.1	$32760$	$864$	$21$	$1$	$1$		$5$	$576$	$0.564360$	$189208196468929/834928640$	$0.93119$	$4.82485$	$[1, 0, 0, -1196, 15760]$	$y^2+xy=x^3-1196x+15760$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 9.24.0-9.a.1.2, 18.72.0-18.a.1.1, $\ldots$	$[]$
910.h1	910k2	910.h	910k	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{7} \cdot 5^{10} \cdot 7 \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.132989085$	$1$		$16$	$2240$	$1.080521$	$19683218700810001/1478750000000$	$0.95936$	$5.50655$	$[1, 0, 0, -5625, -151943]$	$y^2+xy=x^3-5625x-151943$	2.3.0.a.1, 56.6.0.a.1, 260.6.0.?, 3640.12.0.?	$[(-46, 123)]$
910.h2	910k1	910.h	910k	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{14} \cdot 5^{5} \cdot 7^{2} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.066494542$	$1$		$23$	$1120$	$0.733946$	$166021325905681/32614400000$	$0.93577$	$4.80567$	$[1, 0, 0, -1145, 12025]$	$y^2+xy=x^3-1145x+12025$	2.3.0.a.1, 56.6.0.d.1, 130.6.0.?, 3640.12.0.?	$[(10, 35)]$
910.i1	910h1	910.i	910h	$1$	$1$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{17} \cdot 5^{2} \cdot 7^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$728$	$2$	$0$	$0.025707601$	$1$		$18$	$816$	$0.631562$	$-832972004929/14611251200$	$1.10595$	$4.53401$	$[1, 1, 1, -196, 5829]$	$y^2+xy+y=x^3+x^2-196x+5829$	728.2.0.?	$[(9, 65)]$
910.j1	910f1	910.j	910f	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{22} \cdot 5 \cdot 7^{2} \cdot 13^{5} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.105187235$	$1$		$17$	$5280$	$1.538054$	$4307585705106105969/381542350192640$	$1.01074$	$6.29739$	$[1, -1, 1, -33898, 2219177]$	$y^2+xy+y=x^3-x^2-33898x+2219177$	2.3.0.a.1, 56.6.0.c.1, 130.6.0.?, 3640.12.0.?	$[(137, 295)]$
910.j2	910f2	910.j	910f	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ - 2^{11} \cdot 5^{2} \cdot 7 \cdot 13^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$0.210374471$	$1$		$10$	$10560$	$1.884626$	$5964709808210123151/49408483478681600$	$1.10238$	$6.72511$	$[1, -1, 1, 37782, 10304681]$	$y^2+xy+y=x^3-x^2+37782x+10304681$	2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.?	$[(-119, 2087)]$
910.k1	910i2	910.k	910i	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2 \cdot 5^{2} \cdot 7 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$0$	$128$	$-0.174152$	$48587168449/59150$	$0.86593$	$3.61148$	$[1, 1, 1, -76, 223]$	$y^2+xy+y=x^3+x^2-76x+223$	2.3.0.a.1, 56.6.0.a.1, 260.6.0.?, 3640.12.0.?	$[]$
910.k2	910i1	910.k	910i	$2$	$2$	$ 2 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3640$	$12$	$0$	$1$	$1$		$1$	$64$	$-0.520725$	$24137569/12740$	$0.94286$	$2.49496$	$[1, 1, 1, -6, -1]$	$y^2+xy+y=x^3+x^2-6x-1$	2.3.0.a.1, 56.6.0.d.1, 130.6.0.?, 3640.12.0.?	$[]$

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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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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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 (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