LMFDB - Elliptic curves over $\Q$ of conductor 2670

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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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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
2670.a1	2670a1	2670.a	2670a	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{4} \cdot 3^{4} \cdot 5^{2} \cdot 89 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$1780$	$12$	$0$	$0.381491488$	$1$		$11$	$512$	$0.063074$	$326940373369/2883600$	$1.03739$	$3.36041$	$[1, 1, 0, -143, 597]$	$y^2+xy=x^3+x^2-143x+597$	2.3.0.a.1, 20.6.0.b.1, 178.6.0.?, 1780.12.0.?	$[(2, 17)]$
2670.a2	2670a2	2670.a	2670a	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ - 2^{2} \cdot 3^{8} \cdot 5 \cdot 89^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$1780$	$12$	$0$	$0.762982977$	$1$		$8$	$1024$	$0.409648$	$-9116230969/1039393620$	$0.95198$	$3.57697$	$[1, 1, 0, -43, 1537]$	$y^2+xy=x^3+x^2-43x+1537$	2.3.0.a.1, 20.6.0.a.1, 356.6.0.?, 1780.12.0.?	$[(7, 37)]$
2670.b1	2670b3	2670.b	2670b	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{24} \cdot 3^{4} \cdot 5^{6} \cdot 89^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$5340$	$96$	$1$	$1$	$1$		$1$	$82944$	$2.408279$	$117005429346029041260169/14969074876416000000$	$1.02091$	$6.73227$	$[1, 0, 1, -1018969, 349327292]$	$y^2+xy+y=x^3-1018969x+349327292$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 20.6.0.b.1, 60.48.0-60.p.1.15, $\ldots$	$[]$
2670.b2	2670b1	2670.b	2670b	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{8} \cdot 3^{12} \cdot 5^{2} \cdot 89 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$5340$	$96$	$1$	$1$	$1$		$5$	$27648$	$1.858974$	$105803474625631920221209/302708793600$	$1.08341$	$6.71952$	$[1, 0, 1, -985354, 376392956]$	$y^2+xy+y=x^3-985354x+376392956$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 20.6.0.b.1, 60.48.0-60.p.1.16, $\ldots$	$[]$
2670.b3	2670b2	2670.b	2670b	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ - 2^{4} \cdot 3^{24} \cdot 5 \cdot 89^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$5340$	$96$	$1$	$1$	$1$		$4$	$55296$	$2.205547$	$-105674675536486579747609/178969948677280080$	$1.08344$	$6.71973$	$[1, 0, 1, -984954, 376713916]$	$y^2+xy+y=x^3-984954x+376713916$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 20.6.0.a.1, 60.48.0-60.o.1.16, $\ldots$	$[]$
2670.b4	2670b4	2670.b	2670b	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ - 2^{12} \cdot 3^{8} \cdot 5^{3} \cdot 89^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$5340$	$96$	$1$	$1$	$1$		$0$	$165888$	$2.754852$	$404723333046222924179831/1669475455997501952000$	$1.04118$	$7.11933$	$[1, 0, 1, 1541031, 1822863292]$	$y^2+xy+y=x^3+1541031x+1822863292$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 20.6.0.a.1, 60.48.0-60.o.1.15, $\ldots$	$[]$
2670.c1	2670c2	2670.c	2670c	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{13} \cdot 3^{12} \cdot 5 \cdot 89^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3560$	$12$	$0$	$0.564984787$	$1$		$8$	$24960$	$1.746065$	$1174455422712147024721/172422928834560$	$1.00406$	$6.14906$	$[1, 1, 1, -219805, 39568115]$	$y^2+xy+y=x^3+x^2-219805x+39568115$	2.3.0.a.1, 40.6.0.b.1, 356.6.0.?, 3560.12.0.?	$[(295, 564)]$
2670.c2	2670c1	2670.c	2670c	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{26} \cdot 3^{6} \cdot 5^{2} \cdot 89 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$3560$	$12$	$0$	$0.282492393$	$1$		$11$	$12480$	$1.399490$	$373622928668957521/108852255129600$	$0.98070$	$5.12837$	$[1, 1, 1, -15005, 492275]$	$y^2+xy+y=x^3+x^2-15005x+492275$	2.3.0.a.1, 40.6.0.c.1, 178.6.0.?, 3560.12.0.?	$[(-57, 1108)]$
2670.d1	2670d3	2670.d	2670d	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 89 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.102	2B	$712$	$48$	$0$	$1$	$16$	$2$	$0$	$8192$	$1.300259$	$1077773706461706278401/40050$	$1.00377$	$6.13818$	$[1, 1, 1, -213600, -38086065]$	$y^2+xy+y=x^3+x^2-213600x-38086065$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 356.12.0.?, 712.48.0.?	$[]$
2670.d2	2670d2	2670.d	2670d	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{2} \cdot 3^{4} \cdot 5^{4} \cdot 89^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.4	2Cs	$712$	$48$	$0$	$1$	$4$	$2$	$2$	$4096$	$0.953685$	$263129501187842401/1604002500$	$0.97084$	$5.08394$	$[1, 1, 1, -13350, -599265]$	$y^2+xy+y=x^3+x^2-13350x-599265$	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 356.24.0.?, 712.48.0.?	$[]$
2670.d3	2670d4	2670.d	2670d	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ - 2 \cdot 3^{8} \cdot 5^{2} \cdot 89^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.59	2B	$712$	$48$	$0$	$1$	$4$	$2$	$0$	$8192$	$1.300259$	$-248622066042206401/20582592160050$	$0.97225$	$5.09370$	$[1, 1, 1, -13100, -622465]$	$y^2+xy+y=x^3+x^2-13100x-622465$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 712.48.0.?	$[]$
2670.d4	2670d1	2670.d	2670d	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{4} \cdot 3^{2} \cdot 5^{8} \cdot 89 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.53	2B	$712$	$48$	$0$	$1$	$1$		$3$	$2048$	$0.607111$	$67922306042401/5006250000$	$0.92685$	$4.03676$	$[1, 1, 1, -850, -9265]$	$y^2+xy+y=x^3+x^2-850x-9265$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 178.6.0.?, 356.24.0.?, $\ldots$	$[]$
2670.e1	2670f3	2670.e	2670f	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{3} \cdot 3^{6} \cdot 5 \cdot 89^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.8	2B	$3560$	$48$	$0$	$1.175244645$	$1$		$6$	$18432$	$1.559126$	$417315196209220773841/1829563747560$	$1.08289$	$6.01792$	$[1, 0, 0, -155685, -23656743]$	$y^2+xy=x^3-155685x-23656743$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.v.1.1, 712.24.0.?, 3560.48.0.?	$[(-228, 123)]$
2670.e2	2670f2	2670.e	2670f	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{6} \cdot 3^{12} \cdot 5^{2} \cdot 89^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.1	2Cs	$3560$	$48$	$0$	$0.587622322$	$1$		$16$	$9216$	$1.212553$	$106820960574626641/6735270657600$	$1.06271$	$4.96968$	$[1, 0, 0, -9885, -357903]$	$y^2+xy=x^3-9885x-357903$	2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.a.1.4, 356.24.0.?, 3560.48.0.?	$[(-48, -57)]$
2670.e3	2670f1	2670.e	2670f	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{12} \cdot 3^{6} \cdot 5^{4} \cdot 89 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.12.0.7	2B	$3560$	$48$	$0$	$0.293811161$	$1$		$23$	$4608$	$0.865979$	$740750878754641/166095360000$	$0.94642$	$4.33960$	$[1, 0, 0, -1885, 24497]$	$y^2+xy=x^3-1885x+24497$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.bb.1.2, 178.6.0.?, 356.24.0.?, $\ldots$	$[(2, 143)]$
2670.e4	2670f4	2670.e	2670f	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ - 2^{3} \cdot 3^{24} \cdot 5 \cdot 89 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.6	2B	$3560$	$48$	$0$	$1.175244645$	$1$		$4$	$18432$	$1.559126$	$54836918279008559/1005449149872360$	$1.00666$	$5.31911$	$[1, 0, 0, 7915, -1500663]$	$y^2+xy=x^3+7915x-1500663$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.bb.1.5, 356.12.0.?, $\ldots$	$[(112, 835)]$
2670.f1	2670e4	2670.f	2670e	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2 \cdot 3^{4} \cdot 5 \cdot 89^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$10680$	$96$	$1$	$1$	$9$	$3$	$0$	$17280$	$1.700697$	$255719105183305589041/402554845678410$	$0.99879$	$5.95584$	$[1, 0, 0, -132235, -18494185]$	$y^2+xy=x^3-132235x-18494185$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 40.6.0.b.1, 120.48.0.?, $\ldots$	$[]$
2670.f2	2670e3	2670.f	2670e	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 89^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$10680$	$96$	$1$	$1$	$9$	$3$	$1$	$8640$	$1.354122$	$255429141422627949841/634472100$	$0.99876$	$5.95570$	$[1, 0, 0, -132185, -18508875]$	$y^2+xy=x^3-132185x-18508875$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 40.6.0.c.1, 120.48.0.?, $\ldots$	$[]$
2670.f3	2670e2	2670.f	2670e	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{3} \cdot 3^{12} \cdot 5^{3} \cdot 89^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$10680$	$96$	$1$	$1$	$1$		$4$	$5760$	$1.151390$	$33039388998357841/4209544161000$	$0.96386$	$4.82095$	$[1, 0, 0, -6685, 185225]$	$y^2+xy=x^3-6685x+185225$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 40.6.0.b.1, 120.48.0.?, $\ldots$	$[]$
2670.f4	2670e1	2670.f	2670e	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 89 $	$ 2^{6} \cdot 3^{6} \cdot 5^{6} \cdot 89 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$10680$	$96$	$1$	$1$	$1$		$5$	$2880$	$0.804817$	$529102162437841/64881000000$	$0.94114$	$4.29695$	$[1, 0, 0, -1685, -23775]$	$y^2+xy=x^3-1685x-23775$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 40.6.0.c.1, 120.48.0.?, $\ldots$	$[]$

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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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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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