LMFDB - Elliptic curves over $\Q$ of conductor 34969

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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

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Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (22 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Potentially good	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
34969.a1	34969m1	34969.a	34969m	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{8} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$22$	$2$	$0$	$2.349789731$	$1$		$2$	$3855600$	$2.702518$	$-9236754432/1331$	$1.18071$	$5.73490$	$[0, 0, 1, -10106041, -12367267674]$	$y^2+y=x^3-10106041x-12367267674$	22.2.0.a.1	$[(28611, 4808237)]$
34969.b1	34969j1	34969.b	34969j	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{7} $	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$374$	$2$	$0$	$0.939860787$	$1$		$10$	$1036800$	$2.140442$	$37933056/22627$	$0.94788$	$4.66803$	$[0, 0, 1, 244783, -8174004]$	$y^2+y=x^3+244783x-8174004$	374.2.0.?	$[(561, 17484), (6919, 576988)]$
34969.c1	34969i1	34969.c	34969i	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{2} $	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$22$	$2$	$0$	$1.759051205$	$1$		$6$	$38880$	$0.959086$	$1880064/1331$	$1.02432$	$3.29764$	$[0, 0, 1, 2057, 16970]$	$y^2+y=x^3+2057x+16970$	22.2.0.a.1	$[(154, 1996), (55/3, 4645/3)]$
34969.d1	34969l1	34969.d	34969l	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{8} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$22$	$2$	$0$	$3.644136546$	$1$		$2$	$660960$	$2.375694$	$1880064/1331$	$1.02432$	$4.92246$	$[0, 0, 1, 594473, 83374838]$	$y^2+y=x^3+594473x+83374838$	22.2.0.a.1	$[(1156, 48118)]$
34969.e1	34969k1	34969.e	34969k	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{2} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$					$22$	$2$	$0$	$1$	$9$	$3$	$0$	$226800$	$1.285913$	$-9236754432/1331$	$1.18071$	$4.11008$	$[0, 0, 1, -34969, -2517254]$	$y^2+y=x^3-34969x-2517254$	22.2.0.a.1	$[]$
34969.f1	34969g2	34969.f	34969g	$2$	$11$	$ 11^{2} \cdot 17^{2} $	$ - 11^{10} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.4	11B.10.4	$1496$	$480$	$16$	$1$	$1$		$0$	$315744$	$2.097595$	$-121$	$0.94611$	$4.63579$	$[1, 0, 0, -88151, 39371674]$	$y^2+xy=x^3-88151x+39371674$	4.2.0.a.1, 11.60.1.b.1, 44.120.6.b.1, 88.240.16.?, 187.120.1.?, $\ldots$	$[]$
34969.f2	34969g1	34969.f	34969g	$2$	$11$	$ 11^{2} \cdot 17^{2} $	$ - 11^{2} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.3	11B.10.5	$1496$	$480$	$16$	$1$	$1$		$0$	$28704$	$0.898645$	$-24729001$	$0.96853$	$3.71036$	$[1, 0, 0, -8676, -311783]$	$y^2+xy=x^3-8676x-311783$	4.2.0.a.1, 11.60.1.b.2, 44.120.6.b.2, 88.240.16.?, 187.120.1.?, $\ldots$	$[]$
34969.g1	34969c1	34969.g	34969c	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{9} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$3.596142102$	$1$		$2$	$1140480$	$2.609535$	$4096000/4913$	$0.90722$	$5.14958$	$[0, 1, 1, 1282197, -578352615]$	$y^2+y=x^3+x^2+1282197x-578352615$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(403, 1996)]$
34969.h1	34969b1	34969.h	34969b	$1$	$1$	$ 11^{2} \cdot 17^{2} $	$ - 11^{3} \cdot 17^{9} $	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	9.18.0.1	3Ns	$3366$	$72$	$3$	$1.113085534$	$1$		$2$	$103680$	$1.410587$	$4096000/4913$	$0.90722$	$3.77440$	$[0, 1, 1, 10597, 438378]$	$y^2+y=x^3+x^2+10597x+438378$	3.6.0.b.1, 9.18.0.a.1, 33.12.0.a.1, 99.36.0.?, 102.12.0.?, $\ldots$	$[(368, 7369)]$
34969.i1	34969d2	34969.i	34969d	$2$	$3$	$ 11^{2} \cdot 17^{2} $	$ - 11^{7} \cdot 17^{12} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$1122$	$16$	$0$	$1$	$1$		$0$	$1658880$	$2.920002$	$-108394872832/265513259$	$0.97554$	$5.58683$	$[0, -1, 1, -3473587, 5701223692]$	$y^2+y=x^3-x^2-3473587x+5701223692$	3.4.0.a.1, 22.2.0.a.1, 66.8.0.a.1, 102.8.0.?, 561.8.0.?, $\ldots$	$[]$
34969.i2	34969d1	34969.i	34969d	$2$	$3$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{8} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$1122$	$16$	$0$	$1$	$1$		$0$	$552960$	$2.370697$	$134217728/384659$	$1.07792$	$4.92017$	$[0, -1, 1, 373003, -174442533]$	$y^2+y=x^3-x^2+373003x-174442533$	3.4.0.a.1, 22.2.0.a.1, 66.8.0.a.1, 102.8.0.?, 561.8.0.?, $\ldots$	$[]$
34969.j1	34969a2	34969.j	34969a	$2$	$11$	$ 11^{2} \cdot 17^{2} $	$ - 11^{9} \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$	✓							$16.07948293$	$1$		$0$	$228096$	$1.992481$	$-32768$	$1.02512$	$4.68629$	$[0, 1, 1, -256439, -51369785]$	$y^2+y=x^3+x^2-256439x-51369785$		$[(4012235785/2577, 65372961009502/2577)]$
34969.j2	34969a1	34969.j	34969a	$2$	$11$	$ 11^{2} \cdot 17^{2} $	$ - 11^{3} \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-11})$	$-11$	$N(\mathrm{U}(1))$	✓							$1.461771175$	$1$		$0$	$20736$	$0.793534$	$-32768$	$1.02512$	$3.31111$	$[0, 1, 1, -2119, 37824]$	$y^2+y=x^3+x^2-2119x+37824$		$[(184/3, 1576/3)]$
34969.k1	34969f2	34969.k	34969f	$2$	$11$	$ 11^{2} \cdot 17^{2} $	$ - 11^{8} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.3	11B.10.5	$1496$	$480$	$16$	$1$	$1$		$0$	$315744$	$2.097595$	$-24729001$	$0.96853$	$5.08554$	$[1, 0, 1, -1049799, 413933375]$	$y^2+xy+y=x^3-1049799x+413933375$	4.2.0.a.1, 11.60.1.b.2, 44.120.6.b.2, 88.240.16.?, 136.4.0.?, $\ldots$	$[]$
34969.k2	34969f1	34969.k	34969f	$2$	$11$	$ 11^{2} \cdot 17^{2} $	$ - 11^{4} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓	$2, 11$	4.2.0.1, 11.60.1.4	11B.10.4	$1496$	$480$	$16$	$1$	$1$		$0$	$28704$	$0.898645$	$-121$	$0.94611$	$3.26061$	$[1, 0, 1, -729, -29647]$	$y^2+xy+y=x^3-729x-29647$	4.2.0.a.1, 11.60.1.b.1, 44.120.6.b.1, 88.240.16.?, 136.4.0.?, $\ldots$	$[]$
34969.l1	34969e4	34969.l	34969e	$4$	$4$	$ 11^{2} \cdot 17^{2} $	$ 11^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	32.48.0.12	2B	$11968$	$1536$	$53$	$1$	$9$	$3$	$0$	$414720$	$2.238918$	$82483294977/17$	$1.03131$	$5.40254$	$[1, -1, 0, -3171251, 2174464760]$	$y^2+xy=x^3-x^2-3171251x+2174464760$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.j.1, 32.48.0.f.2, $\ldots$	$[]$
34969.l2	34969e2	34969.l	34969e	$4$	$4$	$ 11^{2} \cdot 17^{2} $	$ 11^{6} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.48.0.20	2Cs	$5984$	$1536$	$53$	$1$	$9$	$3$	$2$	$207360$	$1.892345$	$20346417/289$	$1.02963$	$4.60849$	$[1, -1, 0, -198886, 33767487]$	$y^2+xy=x^3-x^2-198886x+33767487$	2.6.0.a.1, 4.12.0.a.1, 8.24.0.f.1, 16.48.0.c.2, 44.24.0-4.a.1.2, $\ldots$	$[]$
34969.l3	34969e1	34969.l	34969e	$4$	$4$	$ 11^{2} \cdot 17^{2} $	$ 11^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	32.48.0.12	2B	$11968$	$1536$	$53$	$1$	$9$	$3$	$1$	$103680$	$1.545771$	$35937/17$	$1.02432$	$4.00261$	$[1, -1, 0, -24041, -607040]$	$y^2+xy=x^3-x^2-24041x-607040$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.j.1, 32.48.0.f.2, $\ldots$	$[]$
34969.l4	34969e3	34969.l	34969e	$4$	$4$	$ 11^{2} \cdot 17^{2} $	$ - 11^{6} \cdot 17^{10} $	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		$2$	16.48.0.76	2B	$11968$	$1536$	$53$	$1$	$9$	$3$	$0$	$414720$	$2.238918$	$-35937/83521$	$1.18071$	$4.79578$	$[1, -1, 0, -24041, 90941802]$	$y^2+xy=x^3-x^2-24041x+90941802$	2.3.0.a.1, 4.12.0.d.1, 8.24.0.t.1, 16.48.0.m.2, 88.48.0.?, $\ldots$	$[]$
34969.m1	34969h3	34969.m	34969h	$3$	$25$	$ 11^{2} \cdot 17^{2} $	$ - 11^{7} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	25.60.0.2	5B.4.2	$9350$	$1200$	$37$	$1$	$1$		$0$	$3072000$	$3.112263$	$-52893159101157376/11$	$1.09296$	$6.68058$	$[0, 1, 1, -273469236, 1740556342399]$	$y^2+y=x^3+x^2-273469236x+1740556342399$	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 110.24.1.?, 170.24.0.?, $\ldots$	$[]$
34969.m2	34969h2	34969.m	34969h	$3$	$25$	$ 11^{2} \cdot 17^{2} $	$ - 11^{11} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	5.60.0.1	5Cs.4.1	$9350$	$1200$	$37$	$1$	$1$		$0$	$614400$	$2.307545$	$-122023936/161051$	$1.01300$	$4.89327$	$[0, 1, 1, -361346, 151310539]$	$y^2+y=x^3+x^2-361346x+151310539$	5.60.0.a.1, 22.2.0.a.1, 110.120.5.?, 170.120.0.?, 275.300.12.?, $\ldots$	$[]$
34969.m3	34969h1	34969.m	34969h	$3$	$25$	$ 11^{2} \cdot 17^{2} $	$ - 11^{7} \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		$5$	25.60.0.1	5B.4.1	$9350$	$1200$	$37$	$1$	$1$		$0$	$122880$	$1.502825$	$-4096/11$	$0.82546$	$3.96039$	$[0, 1, 1, -11656, -1154301]$	$y^2+y=x^3+x^2-11656x-1154301$	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 110.24.1.?, 170.24.0.?, $\ldots$	$[]$

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Elliptic curves over $\Q$
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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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