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

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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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2072.e2	2072c1	2072.e	2072c	$2$	$2$	$ 2^{3} \cdot 7 \cdot 37 $	$ - 2^{10} \cdot 7^{3} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$4.677011045$	$1$		$3$	$864$	$0.344917$	$415292/469567$	$0.92128$	$3.59406$	$[0, -1, 0, 16, -1060]$	$y^2=x^3-x^2+16x-1060$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(298, 5136)]$
4144.a2	4144e1	4144.a	4144e	$2$	$2$	$ 2^{4} \cdot 7 \cdot 37 $	$ - 2^{10} \cdot 7^{3} \cdot 37^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$0.409342356$	$1$		$27$	$1728$	$0.344917$	$415292/469567$	$0.92128$	$3.29498$	$[0, 1, 0, 16, 1060]$	$y^2=x^3+x^2+16x+1060$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(-6, 28), (8, 42)]$
14504.b2	14504f1	14504.b	14504f	$2$	$2$	$ 2^{3} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 7^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$41472$	$1.317873$	$415292/469567$	$0.92128$	$4.08265$	$[0, 1, 0, 768, 362032]$	$y^2=x^3+x^2+768x+362032$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
16576.d2	16576f1	16576.d	16576f	$2$	$2$	$ 2^{6} \cdot 7 \cdot 37 $	$ - 2^{16} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$13824$	$0.691491$	$415292/469567$	$0.92128$	$3.25289$	$[0, 1, 0, 63, -8417]$	$y^2=x^3+x^2+63x-8417$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
16576.t2	16576s1	16576.t	16576s	$2$	$2$	$ 2^{6} \cdot 7 \cdot 37 $	$ - 2^{16} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$13824$	$0.691491$	$415292/469567$	$0.92128$	$3.25289$	$[0, -1, 0, 63, 8417]$	$y^2=x^3-x^2+63x+8417$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
18648.u2	18648z1	18648.u	18648z	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{10} \cdot 3^{6} \cdot 7^{3} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$3.492601757$	$1$		$3$	$20736$	$0.894223$	$415292/469567$	$0.92128$	$3.46133$	$[0, 0, 0, 141, 28478]$	$y^2=x^3+141x+28478$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(259, 4176)]$
29008.n2	29008g1	29008.n	29008g	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 7^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$4$	$2$	$1$	$82944$	$1.317873$	$415292/469567$	$0.92128$	$3.80725$	$[0, -1, 0, 768, -362032]$	$y^2=x^3-x^2+768x-362032$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
37296.cc2	37296ba1	37296.cc	37296ba	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{10} \cdot 3^{6} \cdot 7^{3} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1.361664649$	$1$		$5$	$41472$	$0.894223$	$415292/469567$	$0.92128$	$3.23341$	$[0, 0, 0, 141, -28478]$	$y^2=x^3+141x-28478$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(66, 518)]$
51800.b2	51800s1	51800.b	51800s	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{10} \cdot 5^{6} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$110592$	$1.149635$	$415292/469567$	$0.92128$	$3.41791$	$[0, 1, 0, 392, -131712]$	$y^2=x^3+x^2+392x-131712$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
76664.j2	76664i1	76664.j	76664i	$2$	$2$	$ 2^{3} \cdot 7 \cdot 37^{2} $	$ - 2^{10} \cdot 7^{3} \cdot 37^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$25$	$5$	$1$	$1181952$	$2.150375$	$415292/469567$	$0.92128$	$4.36649$	$[0, -1, 0, 21448, -53432932]$	$y^2=x^3-x^2+21448x-53432932$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
103600.bz2	103600i1	103600.bz	103600i	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{10} \cdot 5^{6} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$221184$	$1.149635$	$415292/469567$	$0.92128$	$3.21276$	$[0, -1, 0, 392, 131712]$	$y^2=x^3-x^2+392x+131712$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
116032.g2	116032bu1	116032.g	116032bu	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 37 $	$ - 2^{16} \cdot 7^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$663552$	$1.664446$	$415292/469567$	$0.92128$	$3.71128$	$[0, 1, 0, 3071, -2893185]$	$y^2=x^3+x^2+3071x-2893185$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
116032.bq2	116032p1	116032.bq	116032p	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 37 $	$ - 2^{16} \cdot 7^{9} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$2.533469087$	$1$		$3$	$663552$	$1.664446$	$415292/469567$	$0.92128$	$3.71128$	$[0, -1, 0, 3071, 2893185]$	$y^2=x^3-x^2+3071x+2893185$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(4527, 304584)]$
130536.o2	130536e1	130536.o	130536e	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 3^{6} \cdot 7^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$995328$	$1.867178$	$415292/469567$	$0.92128$	$3.88070$	$[0, 0, 0, 6909, -9767954]$	$y^2=x^3+6909x-9767954$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
149184.bs2	149184eg1	149184.bs	149184eg	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{16} \cdot 3^{6} \cdot 7^{3} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$3.238946201$	$1$		$3$	$331776$	$1.240797$	$415292/469567$	$0.92128$	$3.20625$	$[0, 0, 0, 564, 227824]$	$y^2=x^3+564x+227824$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(104, 1188)]$
149184.bv2	149184q1	149184.bv	149184q	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{16} \cdot 3^{6} \cdot 7^{3} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1.698446079$	$1$		$5$	$331776$	$1.240797$	$415292/469567$	$0.92128$	$3.20625$	$[0, 0, 0, 564, -227824]$	$y^2=x^3+564x-227824$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(76, 504)]$
153328.e2	153328j1	153328.e	153328j	$2$	$2$	$ 2^{4} \cdot 7 \cdot 37^{2} $	$ - 2^{10} \cdot 7^{3} \cdot 37^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$2363904$	$2.150375$	$415292/469567$	$0.92128$	$4.11301$	$[0, 1, 0, 21448, 53432932]$	$y^2=x^3+x^2+21448x+53432932$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
250712.p2	250712p1	250712.p	250712p	$2$	$2$	$ 2^{3} \cdot 7 \cdot 11^{2} \cdot 37 $	$ - 2^{10} \cdot 7^{3} \cdot 11^{6} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$1105920$	$1.543865$	$415292/469567$	$0.92128$	$3.36490$	$[0, -1, 0, 1896, 1403228]$	$y^2=x^3-x^2+1896x+1403228$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
261072.ci2	261072ci1	261072.ci	261072ci	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 3^{6} \cdot 7^{9} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$3.726813778$	$1$		$3$	$1990656$	$1.867178$	$415292/469567$	$0.92128$	$3.66504$	$[0, 0, 0, 6909, 9767954]$	$y^2=x^3+6909x+9767954$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[(85, 3312)]$
350168.i2	350168i1	350168.i	350168i	$2$	$2$	$ 2^{3} \cdot 7 \cdot 13^{2} \cdot 37 $	$ - 2^{10} \cdot 7^{3} \cdot 13^{6} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$1658880$	$1.627392$	$415292/469567$	$0.92128$	$3.35535$	$[0, -1, 0, 2648, -2318148]$	$y^2=x^3-x^2+2648x-2318148$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
362600.ct2	362600ct1	362600.ct	362600ct	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{10} \cdot 5^{6} \cdot 7^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$5308416$	$2.122593$	$415292/469567$	$0.92128$	$3.81042$	$[0, -1, 0, 19192, 45215612]$	$y^2=x^3-x^2+19192x+45215612$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
414400.s2	414400s1	414400.s	414400s	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{16} \cdot 5^{6} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$1769472$	$1.496210$	$415292/469567$	$0.92128$	$3.18996$	$[0, 1, 0, 1567, 1055263]$	$y^2=x^3+x^2+1567x+1055263$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
414400.fb2	414400fb1	414400.fb	414400fb	$2$	$2$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{16} \cdot 5^{6} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$1769472$	$1.496210$	$415292/469567$	$0.92128$	$3.18996$	$[0, -1, 0, 1567, -1055263]$	$y^2=x^3-x^2+1567x-1055263$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$
466200.cr2	466200cr1	466200.cr	466200cr	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{10} \cdot 3^{6} \cdot 5^{6} \cdot 7^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$2072$	$12$	$0$	$1$	$1$		$1$	$2654208$	$1.698942$	$415292/469567$	$0.92128$	$3.34756$	$[0, 0, 0, 3525, 3559750]$	$y^2=x^3+3525x+3559750$	2.3.0.a.1, 14.6.0.b.1, 296.6.0.?, 2072.12.0.?	$[]$

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Elliptic curves over $\Q$
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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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