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	Manin constant

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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	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
10920.j3	10920n3	10920.j	10920n	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.24.0.6	2Cs	$10920$	$192$	$1$	$0.910119513$	$1$	$13$	$32768$	$1.369267$	$278944461825124/70849130625$	$0.93241$	$4.32265$	$[0, -1, 0, -13720, 467932]$	$y^2=x^3-x^2-13720x+467932$	2.6.0.a.1, 4.24.0-4.b.1.1, 56.48.0-56.e.1.9, 104.48.0.?, 120.48.0.?, $\ldots$	$[(129, 910)]$
21840.ce3	21840s3	21840.ce	21840s	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.24.0.5	2Cs	$10920$	$192$	$1$	$1$	$1$	$7$	$65536$	$1.369267$	$278944461825124/70849130625$	$0.93241$	$4.02277$	$[0, 1, 0, -13720, -467932]$	$y^2=x^3+x^2-13720x-467932$	2.6.0.a.1, 4.24.0-4.b.1.3, 56.48.0-56.e.1.1, 104.48.0.?, 120.48.0.?, $\ldots$	$[ ]$
32760.u3	32760n3	32760.u	32760n	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$262144$	$1.918573$	$278944461825124/70849130625$	$0.93241$	$4.49989$	$[0, 0, 0, -123483, -12510682]$	$y^2=x^3-123483x-12510682$	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.1, 40.24.0-4.b.1.7, 56.24.0.e.1, $\ldots$	$[ ]$
54600.bl3	54600t3	54600.bl	54600t	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{4} \cdot 5^{10} \cdot 7^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$786432$	$2.173985$	$278944461825124/70849130625$	$0.93241$	$4.57014$	$[0, 1, 0, -343008, 57805488]$	$y^2=x^3+x^2-343008x+57805488$	2.6.0.a.1, 4.12.0.b.1, 20.24.0-4.b.1.1, 24.24.0-4.b.1.7, 56.24.0.e.1, $\ldots$	$[ ]$
65520.c3	65520s3	65520.c	65520s	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$0.814429978$	$1$	$17$	$524288$	$1.918573$	$278944461825124/70849130625$	$0.93241$	$4.21864$	$[0, 0, 0, -123483, 12510682]$	$y^2=x^3-123483x+12510682$	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.3, 40.24.0-4.b.1.2, 56.24.0.e.1, $\ldots$	$[(-43, 4212)]$
76440.bn3	76440cs3	76440.bn	76440cs	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.19	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$1572864$	$2.342220$	$278944461825124/70849130625$	$0.93241$	$4.61293$	$[0, 1, 0, -672296, -159156096]$	$y^2=x^3+x^2-672296x-159156096$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.6, 28.24.0-4.b.1.1, 56.48.0-56.e.1.5, $\ldots$	$[ ]$
87360.e3	87360ea3	87360.e	87360ea	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{16} \cdot 3^{4} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.21	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$524288$	$1.715839$	$278944461825124/70849130625$	$0.93241$	$3.89815$	$[0, -1, 0, -54881, -3688575]$	$y^2=x^3-x^2-54881x-3688575$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.2, 28.24.0-4.b.1.2, 56.48.0-56.e.1.10, $\ldots$	$[ ]$
87360.fi3	87360ch3	87360.fi	87360ch	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 $	$ 2^{16} \cdot 3^{4} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.20	2Cs	$10920$	$192$	$1$	$2.555791709$	$1$	$9$	$524288$	$1.715839$	$278944461825124/70849130625$	$0.93241$	$3.89815$	$[0, 1, 0, -54881, 3688575]$	$y^2=x^3+x^2-54881x+3688575$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.11, 28.24.0-4.b.1.2, 56.48.0-56.e.1.3, $\ldots$	$[(61, 756)]$
109200.dg3	109200o3	109200.dg	109200o	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{4} \cdot 5^{10} \cdot 7^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$1572864$	$2.173985$	$278944461825124/70849130625$	$0.93241$	$4.29708$	$[0, -1, 0, -343008, -57805488]$	$y^2=x^3-x^2-343008x-57805488$	2.6.0.a.1, 4.12.0.b.1, 20.24.0-4.b.1.3, 24.24.0-4.b.1.2, 56.24.0.e.1, $\ldots$	$[ ]$
141960.f3	141960cn4	141960.f	141960cn	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} $	$ 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{2} \cdot 13^{10} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.11	2Cs	$10920$	$192$	$1$	$9.662930222$	$1$	$3$	$5505024$	$2.651741$	$278944461825124/70849130625$	$0.93241$	$4.68531$	$[0, -1, 0, -2318736, 1018771740]$	$y^2=x^3-x^2-2318736x+1018771740$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.8, 52.24.0-4.b.1.1, 56.48.0-56.e.1.20, $\ldots$	$[(-12399/5, 5654826/5)]$
152880.cg3	152880ik4	152880.cg	152880ik	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{8} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.19	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$3145728$	$2.342220$	$278944461825124/70849130625$	$0.93241$	$4.34508$	$[0, -1, 0, -672296, 159156096]$	$y^2=x^3-x^2-672296x+159156096$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.6, 28.24.0-4.b.1.3, 56.48.0-56.e.1.11, $\ldots$	$[ ]$
163800.cg3	163800bw3	163800.cg	163800bw	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{10} \cdot 5^{10} \cdot 7^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.11	2Cs	$10920$	$192$	$1$	$8.527104303$	$1$	$3$	$6291456$	$2.723293$	$278944461825124/70849130625$	$0.93241$	$4.70098$	$[0, 0, 0, -3087075, -1563835250]$	$y^2=x^3-3087075x-1563835250$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.8, 56.48.0-56.e.1.6, 60.24.0-4.b.1.1, $\ldots$	$[(348355/3, 205390000/3)]$
229320.er3	229320dj4	229320.er	229320dj	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$12582912$	$2.891529$	$278944461825124/70849130625$	$0.93241$	$4.73639$	$[0, 0, 0, -6050667, 4291163926]$	$y^2=x^3-6050667x+4291163926$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.6, 40.24.0-4.b.1.8, 56.24.0.e.1, $\ldots$	$[ ]$
262080.jx3	262080jx4	262080.jx	262080jx	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ 2^{16} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$4194304$	$2.265148$	$278944461825124/70849130625$	$0.93241$	$4.08323$	$[0, 0, 0, -493932, 100085456]$	$y^2=x^3-493932x+100085456$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.1, 40.24.0-4.b.1.8, 56.24.0.e.1, $\ldots$	$[ ]$
262080.kr3	262080kr3	262080.kr	262080kr	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 $	$ 2^{16} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$4194304$	$2.265148$	$278944461825124/70849130625$	$0.93241$	$4.08323$	$[0, 0, 0, -493932, -100085456]$	$y^2=x^3-493932x-100085456$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.11, 40.24.0-4.b.1.3, 56.24.0.e.1, $\ldots$	$[ ]$
283920.fn3	283920fn3	283920.fn	283920fn	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} $	$ 2^{10} \cdot 3^{4} \cdot 5^{4} \cdot 7^{2} \cdot 13^{10} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.17	2Cs	$10920$	$192$	$1$	$4.788137017$	$1$	$7$	$11010048$	$2.651741$	$278944461825124/70849130625$	$0.93241$	$4.42667$	$[0, 1, 0, -2318736, -1018771740]$	$y^2=x^3+x^2-2318736x-1018771740$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 52.24.0-4.b.1.3, 56.48.0-56.e.1.15, $\ldots$	$[(-1176, 9114)]$
327600.ht3	327600ht4	327600.ht	327600ht	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 $	$ 2^{10} \cdot 3^{10} \cdot 5^{10} \cdot 7^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.17	2Cs	$10920$	$192$	$1$	$3.110892839$	$1$	$9$	$12582912$	$2.723293$	$278944461825124/70849130625$	$0.93241$	$4.44439$	$[0, 0, 0, -3087075, 1563835250]$	$y^2=x^3-3087075x+1563835250$	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 56.48.0-56.e.1.4, 60.24.0-4.b.1.3, $\ldots$	$[(530, 8750)]$
382200.v3	382200v3	382200.v	382200v	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ 2^{10} \cdot 3^{4} \cdot 5^{10} \cdot 7^{8} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$5.485957812$	$1$	$5$	$37748736$	$3.146942$	$278944461825124/70849130625$	$0.93241$	$4.78661$	$[0, -1, 0, -16807408, -19860897188]$	$y^2=x^3-x^2-16807408x-19860897188$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.8, 40.24.0-4.b.1.6, 56.24.0.e.1, $\ldots$	$[(55557, 13058500)]$
425880.cx3	425880cx3	425880.cx	425880cx	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} $	$ 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7^{2} \cdot 13^{10} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$1$	$1$	$3$	$44040192$	$3.201046$	$278944461825124/70849130625$	$0.93241$	$4.79674$	$[0, 0, 0, -20868627, -27485968354]$	$y^2=x^3-20868627x-27485968354$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.7, 40.24.0-4.b.1.5, 56.24.0.e.1, $\ldots$	$[ ]$
436800.eu3	436800eu4	436800.eu	436800eu	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ 2^{16} \cdot 3^{4} \cdot 5^{10} \cdot 7^{2} \cdot 13^{4} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$4.833963321$	$1$	$23$	$12582912$	$2.520557$	$278944461825124/70849130625$	$0.93241$	$4.15862$	$[0, -1, 0, -1372033, 463815937]$	$y^2=x^3-x^2-1372033x+463815937$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.3, 40.24.0-4.b.1.11, 56.24.0.e.1, $\ldots$	$[(312, 8125), (1833, 64064)]$
436800.qa3	436800qa3	436800.qa	436800qa	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $	$ 2^{16} \cdot 3^{4} \cdot 5^{10} \cdot 7^{2} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$2.234140133$	$1$	$9$	$12582912$	$2.520557$	$278944461825124/70849130625$	$0.93241$	$4.15862$	$[0, 1, 0, -1372033, -463815937]$	$y^2=x^3+x^2-1372033x-463815937$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.8, 40.24.0-4.b.1.1, 56.24.0.e.1, $\ldots$	$[(-793, 11232)]$
458640.if3	458640if3	458640.if	458640if	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 7^{8} \cdot 13^{4} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.3	2Cs	$10920$	$192$	$1$	$5.633044319$	$1$	$25$	$25165824$	$2.891529$	$278944461825124/70849130625$	$0.93241$	$4.48455$	$[0, 0, 0, -6050667, -4291163926]$	$y^2=x^3-6050667x-4291163926$	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.6, 40.24.0-4.b.1.3, 56.24.0.e.1, $\ldots$	$[(-917, 22050), (9373, 873180)]$

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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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