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 (30 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
4312.a2	4312l1	4312.a	4312l	$2$	$2$	$ 2^{3} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 7^{3} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$0.336514112$	$1$		$29$	$1536$	$0.089909$	$-1272112/121$	$0.78104$	$3.05781$	$[0, 1, 0, -100, 384]$	$y^2=x^3+x^2-100x+384$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(2, 14), (6, 6)]$
4312.k2	4312k1	4312.k	4312k	$2$	$2$	$ 2^{3} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$4$	$2$	$1$	$10752$	$1.062864$	$-1272112/121$	$0.78104$	$4.45287$	$[0, -1, 0, -4916, -141532]$	$y^2=x^3-x^2-4916x-141532$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
8624.h2	8624d1	8624.h	8624d	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$21504$	$1.062864$	$-1272112/121$	$0.78104$	$4.11228$	$[0, 1, 0, -4916, 141532]$	$y^2=x^3+x^2-4916x+141532$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
8624.x2	8624c1	8624.x	8624c	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 7^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$3072$	$0.089909$	$-1272112/121$	$0.78104$	$2.82393$	$[0, -1, 0, -100, -384]$	$y^2=x^3-x^2-100x-384$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
34496.j2	34496z1	34496.j	34496z	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$172032$	$1.409437$	$-1272112/121$	$0.78104$	$3.96471$	$[0, 1, 0, -19665, -1151921]$	$y^2=x^3+x^2-19665x-1151921$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
34496.v2	34496dq1	34496.v	34496dq	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 7^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$24576$	$0.436482$	$-1272112/121$	$0.78104$	$2.84729$	$[0, 1, 0, -401, -3473]$	$y^2=x^3+x^2-401x-3473$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
34496.cw2	34496dm1	34496.cw	34496dm	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$172032$	$1.409437$	$-1272112/121$	$0.78104$	$3.96471$	$[0, -1, 0, -19665, 1151921]$	$y^2=x^3-x^2-19665x+1151921$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
34496.dh2	34496w1	34496.dh	34496w	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 7^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$24576$	$0.436482$	$-1272112/121$	$0.78104$	$2.84729$	$[0, -1, 0, -401, 3473]$	$y^2=x^3-x^2-401x+3473$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
38808.a2	38808bb1	38808.a	38808bb	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{9} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$2.086332943$	$1$		$5$	$258048$	$1.612169$	$-1272112/121$	$0.78104$	$4.15075$	$[0, 0, 0, -44247, 3865610]$	$y^2=x^3-44247x+3865610$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(98, 686)]$
38808.cp2	38808ba1	38808.cp	38808ba	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{3} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$4.454600309$	$1$		$3$	$36864$	$0.639215$	$-1272112/121$	$0.78104$	$3.04579$	$[0, 0, 0, -903, -11270]$	$y^2=x^3-903x-11270$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(210, 3010)]$
47432.b2	47432l1	47432.b	47432l	$2$	$2$	$ 2^{3} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{8} \cdot 7^{3} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$3.278708115$	$1$		$3$	$184320$	$1.288857$	$-1272112/121$	$0.78104$	$3.71305$	$[0, 1, 0, -12140, -559616]$	$y^2=x^3+x^2-12140x-559616$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(227, 2904)]$
47432.x2	47432j1	47432.x	47432j	$2$	$2$	$ 2^{3} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{8} \cdot 7^{9} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$11.10289895$	$1$		$1$	$1290240$	$2.261810$	$-1272112/121$	$0.78104$	$4.79742$	$[0, -1, 0, -594876, 190758548]$	$y^2=x^3-x^2-594876x+190758548$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(726881/5, 619492896/5)]$
77616.k2	77616cr1	77616.k	77616cr	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$516096$	$1.612169$	$-1272112/121$	$0.78104$	$3.89523$	$[0, 0, 0, -44247, -3865610]$	$y^2=x^3-44247x-3865610$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
77616.gv2	77616cq1	77616.gv	77616cq	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$73728$	$0.639215$	$-1272112/121$	$0.78104$	$2.85829$	$[0, 0, 0, -903, 11270]$	$y^2=x^3-903x+11270$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
94864.v2	94864z1	94864.v	94864z	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{8} \cdot 7^{9} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$18.35064920$	$1$		$1$	$2580480$	$2.261810$	$-1272112/121$	$0.78104$	$4.50726$	$[0, 1, 0, -594876, -190758548]$	$y^2=x^3+x^2-594876x-190758548$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(6241257794/1115, 486889065772472/1115)]$
94864.cs2	94864w1	94864.cs	94864w	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{8} \cdot 7^{3} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$2.422945364$	$1$		$1$	$368640$	$1.288857$	$-1272112/121$	$0.78104$	$3.48848$	$[0, -1, 0, -12140, 559616]$	$y^2=x^3-x^2-12140x+559616$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(181/2, 2541/2)]$
107800.m2	107800t1	107800.m	107800t	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5^{6} \cdot 7^{9} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$9.123393882$	$1$		$1$	$860160$	$1.867582$	$-1272112/121$	$0.78104$	$4.04929$	$[0, 1, 0, -122908, -17937312]$	$y^2=x^3+x^2-122908x-17937312$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(25259/5, 3729748/5)]$
107800.ch2	107800q1	107800.ch	107800q	$2$	$2$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5^{6} \cdot 7^{3} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$2.558062645$	$1$		$3$	$122880$	$0.894628$	$-1272112/121$	$0.78104$	$3.04175$	$[0, -1, 0, -2508, 53012]$	$y^2=x^3-x^2-2508x+53012$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(41, 132)]$
215600.x2	215600ge1	215600.x	215600ge	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5^{6} \cdot 7^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$245760$	$0.894628$	$-1272112/121$	$0.78104$	$2.87007$	$[0, 1, 0, -2508, -53012]$	$y^2=x^3+x^2-2508x-53012$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
215600.gq2	215600ib1	215600.gq	215600ib	$2$	$2$	$ 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{8} \cdot 5^{6} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$1720320$	$1.867582$	$-1272112/121$	$0.78104$	$3.82075$	$[0, -1, 0, -122908, 17937312]$	$y^2=x^3-x^2-122908x+17937312$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
310464.g2	310464g1	310464.g	310464g	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 3^{6} \cdot 7^{3} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1.571971829$	$1$		$17$	$589824$	$0.985788$	$-1272112/121$	$0.78104$	$2.87382$	$[0, 0, 0, -3612, 90160]$	$y^2=x^3-3612x+90160$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(18, 176), (29, 99)]$
310464.t2	310464t1	310464.t	310464t	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 3^{6} \cdot 7^{3} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$589824$	$0.985788$	$-1272112/121$	$0.78104$	$2.87382$	$[0, 0, 0, -3612, -90160]$	$y^2=x^3-3612x-90160$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
310464.rr2	310464rr1	310464.rr	310464rr	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 3^{6} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$4$	$2$	$1$	$4128768$	$1.958744$	$-1272112/121$	$0.78104$	$3.79709$	$[0, 0, 0, -176988, -30924880]$	$y^2=x^3-176988x-30924880$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
310464.sg2	310464sg1	310464.sg	310464sg	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{14} \cdot 3^{6} \cdot 7^{9} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$4128768$	$1.958744$	$-1272112/121$	$0.78104$	$3.79709$	$[0, 0, 0, -176988, 30924880]$	$y^2=x^3-176988x+30924880$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
379456.r2	379456r1	379456.r	379456r	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{14} \cdot 7^{9} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$2.663026184$	$1$		$5$	$20643840$	$2.608383$	$-1272112/121$	$0.78104$	$4.34461$	$[0, 1, 0, -2379505, 1523688879]$	$y^2=x^3+x^2-2379505x+1523688879$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(865, 10648)]$
379456.cd2	379456cd1	379456.cd	379456cd	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{14} \cdot 7^{3} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$2949120$	$1.635429$	$-1272112/121$	$0.78104$	$3.43576$	$[0, 1, 0, -48561, 4428367]$	$y^2=x^3+x^2-48561x+4428367$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
379456.hu2	379456hu1	379456.hu	379456hu	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{14} \cdot 7^{9} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$1$	$1$		$1$	$20643840$	$2.608383$	$-1272112/121$	$0.78104$	$4.34461$	$[0, -1, 0, -2379505, -1523688879]$	$y^2=x^3-x^2-2379505x-1523688879$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[]$
379456.jg2	379456jg1	379456.jg	379456jg	$2$	$2$	$ 2^{6} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{14} \cdot 7^{3} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$13.25754988$	$1$		$1$	$2949120$	$1.635429$	$-1272112/121$	$0.78104$	$3.43576$	$[0, -1, 0, -48561, -4428367]$	$y^2=x^3-x^2-48561x-4428367$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(41707087/21, 269346484000/21)]$
426888.g2	426888g1	426888.g	426888g	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{8} \cdot 3^{6} \cdot 7^{9} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$5.048542738$	$1$		$5$	$30965760$	$2.811119$	$-1272112/121$	$0.78104$	$4.49279$	$[0, 0, 0, -5353887, -5145126910]$	$y^2=x^3-5353887x-5145126910$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(2717, 19118)]$
426888.hw2	426888hw1	426888.hw	426888hw	$2$	$2$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 11^{2} $	$ - 2^{8} \cdot 3^{6} \cdot 7^{3} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$308$	$12$	$0$	$2.169765110$	$1$		$3$	$4423680$	$1.838161$	$-1272112/121$	$0.78104$	$3.59220$	$[0, 0, 0, -109263, 15000370]$	$y^2=x^3-109263x+15000370$	2.3.0.a.1, 14.6.0.b.1, 44.6.0.d.1, 308.12.0.?	$[(165, 1210)]$

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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 (30 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.

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