LMFDB - Elliptic curve search results

Refine search

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

Intrinsic torsion order

			Sort order	Select

Results (28 matches)

Download displayed columns for results to

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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
3328.c1	3328d2	3328.c	3328d	$2$	$5$	$ 2^{8} \cdot 13 $	$ - 2^{9} \cdot 13^{5} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$0.382325592$	$1$		$16$	$960$	$0.267522$	$-85184/371293$	$1.11420$	$3.26973$	$1$	$[0, -1, 0, -7, -661]$	$y^2=x^3-x^2-7x-661$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(49, 338), (10, 13)]$	$1$
3328.f2	3328g2	3328.f	3328g	$2$	$5$	$ 2^{8} \cdot 13 $	$ - 2^{15} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$1$	$1$		$0$	$1920$	$0.614096$	$-85184/371293$	$1.11420$	$3.78253$	$1$	$[0, -1, 0, -29, 5317]$	$y^2=x^3-x^2-29x+5317$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
3328.g2	3328k2	3328.g	3328k	$2$	$5$	$ 2^{8} \cdot 13 $	$ - 2^{9} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$0.250103036$	$1$		$2$	$960$	$0.267522$	$-85184/371293$	$1.11420$	$3.26973$	$1$	$[0, 1, 0, -7, 661]$	$y^2=x^3+x^2-7x+661$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(3, 26)]$	$1$
3328.j1	3328b2	3328.j	3328b	$2$	$5$	$ 2^{8} \cdot 13 $	$ - 2^{15} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$3.684640651$	$1$		$2$	$1920$	$0.614096$	$-85184/371293$	$1.11420$	$3.78253$	$1$	$[0, 1, 0, -29, -5317]$	$y^2=x^3+x^2-29x-5317$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(101, 1016)]$	$1$
29952.a2	29952c2	29952.a	29952c	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13 $	$ - 2^{15} \cdot 3^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$1$	$1$		$0$	$57600$	$1.163403$	$-85184/371293$	$1.11420$	$3.61572$	$1$	$[0, 0, 0, -264, 143296]$	$y^2=x^3-264x+143296$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
29952.b1	29952i2	29952.b	29952i	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13 $	$ - 2^{15} \cdot 3^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$7.443408726$	$1$		$0$	$57600$	$1.163403$	$-85184/371293$	$1.11420$	$3.61572$	$1$	$[0, 0, 0, -264, -143296]$	$y^2=x^3-264x-143296$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[(2984/7, 88432/7)]$	$1$
29952.k2	29952f2	29952.k	29952f	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13 $	$ - 2^{9} \cdot 3^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$0.789455425$	$1$		$2$	$28800$	$0.816828$	$-85184/371293$	$1.11420$	$3.21223$	$1$	$[0, 0, 0, -66, 17912]$	$y^2=x^3-66x+17912$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[(23, 169)]$	$1$
29952.l1	29952l2	29952.l	29952l	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13 $	$ - 2^{9} \cdot 3^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$1$	$1$		$0$	$28800$	$0.816828$	$-85184/371293$	$1.11420$	$3.21223$	$1$	$[0, 0, 0, -66, -17912]$	$y^2=x^3-66x-17912$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
43264.d2	43264s2	43264.d	43264s	$2$	$5$	$ 2^{8} \cdot 13^{2} $	$ - 2^{15} \cdot 13^{11} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$2.505500628$	$1$		$6$	$322560$	$1.896570$	$-85184/371293$	$1.11420$	$4.31533$	$1$	$[0, -1, 0, -4957, 11661701]$	$y^2=x^3-x^2-4957x+11661701$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(932, 28561), (-173, 2704)]$	$1$
43264.k1	43264e2	43264.k	43264e	$2$	$5$	$ 2^{8} \cdot 13^{2} $	$ - 2^{9} \cdot 13^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$7.303620561$	$1$		$0$	$161280$	$1.549997$	$-85184/371293$	$1.11420$	$3.92574$	$1$	$[0, -1, 0, -1239, -1457093]$	$y^2=x^3-x^2-1239x-1457093$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(15586/7, 1885871/7)]$	$1$
43264.r1	43264c2	43264.r	43264c	$2$	$5$	$ 2^{8} \cdot 13^{2} $	$ - 2^{15} \cdot 13^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$4.110290300$	$1$		$0$	$322560$	$1.896570$	$-85184/371293$	$1.11420$	$4.31533$	$1$	$[0, 1, 0, -4957, -11661701]$	$y^2=x^3+x^2-4957x-11661701$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(11454/7, 28561/7)]$	$1$
43264.y2	43264q2	43264.y	43264q	$2$	$5$	$ 2^{8} \cdot 13^{2} $	$ - 2^{9} \cdot 13^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$1$	$1$		$0$	$161280$	$1.549997$	$-85184/371293$	$1.11420$	$3.92574$	$1$	$[0, 1, 0, -1239, 1457093]$	$y^2=x^3+x^2-1239x+1457093$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
83200.i2	83200x2	83200.i	83200x	$2$	$5$	$ 2^{8} \cdot 5^{2} \cdot 13 $	$ - 2^{9} \cdot 5^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$1$	$1$		$0$	$103680$	$1.072241$	$-85184/371293$	$1.11420$	$3.19309$	$1$	$[0, -1, 0, -183, 82987]$	$y^2=x^3-x^2-183x+82987$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
83200.p1	83200k2	83200.p	83200k	$2$	$5$	$ 2^{8} \cdot 5^{2} \cdot 13 $	$ - 2^{15} \cdot 5^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$1$	$1$		$0$	$207360$	$1.418814$	$-85184/371293$	$1.11420$	$3.56019$	$1$	$[0, -1, 0, -733, -663163]$	$y^2=x^3-x^2-733x-663163$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
83200.u2	83200bc2	83200.u	83200bc	$2$	$5$	$ 2^{8} \cdot 5^{2} \cdot 13 $	$ - 2^{15} \cdot 5^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$1.412940112$	$1$		$2$	$207360$	$1.418814$	$-85184/371293$	$1.11420$	$3.56019$	$1$	$[0, 1, 0, -733, 663163]$	$y^2=x^3+x^2-733x+663163$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(189, 2704)]$	$1$
83200.bb1	83200b2	83200.bb	83200b	$2$	$5$	$ 2^{8} \cdot 5^{2} \cdot 13 $	$ - 2^{9} \cdot 5^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$1040$	$48$	$1$	$12.28717172$	$1$		$0$	$103680$	$1.072241$	$-85184/371293$	$1.11420$	$3.19309$	$1$	$[0, 1, 0, -183, -82987]$	$y^2=x^3+x^2-183x-82987$	5.6.0.a.1, 40.12.0.bp.2, 80.24.0.?, 104.2.0.?, 260.12.0.?, $\ldots$	$[(141604/49, 39868669/49)]$	$1$
163072.p2	163072bn2	163072.p	163072bn	$2$	$5$	$ 2^{8} \cdot 7^{2} \cdot 13 $	$ - 2^{15} \cdot 7^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$7280$	$48$	$1$	$1.150273765$	$1$		$2$	$633600$	$1.587051$	$-85184/371293$	$1.11420$	$3.52878$	$1$	$[0, -1, 0, -1437, 1820869]$	$y^2=x^3-x^2-1437x+1820869$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[(-5, 1352)]$	$1$
163072.ba1	163072o2	163072.ba	163072o	$2$	$5$	$ 2^{8} \cdot 7^{2} \cdot 13 $	$ - 2^{9} \cdot 7^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$7280$	$48$	$1$	$11.76793556$	$1$		$0$	$316800$	$1.240477$	$-85184/371293$	$1.11420$	$3.18227$	$1$	$[0, -1, 0, -359, -227429]$	$y^2=x^3-x^2-359x-227429$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[(108425/41, 8036006/41)]$	$1$
163072.bl1	163072u2	163072.bl	163072u	$2$	$5$	$ 2^{8} \cdot 7^{2} \cdot 13 $	$ - 2^{15} \cdot 7^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$7280$	$48$	$1$	$1$	$1$		$0$	$633600$	$1.587051$	$-85184/371293$	$1.11420$	$3.52878$	$1$	$[0, 1, 0, -1437, -1820869]$	$y^2=x^3+x^2-1437x-1820869$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[ ]$	$1$
163072.bw2	163072cd2	163072.bw	163072cd	$2$	$5$	$ 2^{8} \cdot 7^{2} \cdot 13 $	$ - 2^{9} \cdot 7^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$7280$	$48$	$1$	$1$	$4$	$2$	$0$	$316800$	$1.240477$	$-85184/371293$	$1.11420$	$3.18227$	$1$	$[0, 1, 0, -359, 227429]$	$y^2=x^3+x^2-359x+227429$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[ ]$	$1$
389376.f1	389376f2	389376.f	389376f	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 13^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$7.924793186$	$1$		$2$	$4838400$	$2.099304$	$-85184/371293$	$1.11420$	$3.76773$	$1$	$[0, 0, 0, -11154, -39352664]$	$y^2=x^3-11154x-39352664$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[(50622, 11389586)]$	$1$
389376.g2	389376g2	389376.g	389376g	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 13^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$1$	$4$	$2$	$0$	$4838400$	$2.099304$	$-85184/371293$	$1.11420$	$3.76773$	$1$	$[0, 0, 0, -11154, 39352664]$	$y^2=x^3-11154x+39352664$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
389376.bx1	389376bx2	389376.bx	389376bx	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{6} \cdot 13^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$13.56801934$	$1$		$0$	$9676800$	$2.445877$	$-85184/371293$	$1.11420$	$4.09081$	$1$	$[0, 0, 0, -44616, -314821312]$	$y^2=x^3-44616x-314821312$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[(147085913/457, 167260099201/457)]$	$1$
389376.by2	389376by2	389376.by	389376by	$2$	$5$	$ 2^{8} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{6} \cdot 13^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$3120$	$48$	$1$	$1$	$4$	$2$	$0$	$9676800$	$2.445877$	$-85184/371293$	$1.11420$	$4.09081$	$1$	$[0, 0, 0, -44616, 314821312]$	$y^2=x^3-44616x+314821312$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 240.24.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
402688.n2	402688n2	402688.n	402688n	$2$	$5$	$ 2^{8} \cdot 11^{2} \cdot 13 $	$ - 2^{9} \cdot 11^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$11440$	$48$	$1$	$1$	$1$		$0$	$1382400$	$1.466469$	$-85184/371293$	$1.11420$	$3.16950$	$1$	$[0, -1, 0, -887, 883291]$	$y^2=x^3-x^2-887x+883291$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[ ]$	$1$
402688.s1	402688s2	402688.s	402688s	$2$	$5$	$ 2^{8} \cdot 11^{2} \cdot 13 $	$ - 2^{15} \cdot 11^{6} \cdot 13^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$11440$	$48$	$1$	$1$	$1$		$0$	$2764800$	$1.813044$	$-85184/371293$	$1.11420$	$3.49175$	$1$	$[0, -1, 0, -3549, -7062779]$	$y^2=x^3-x^2-3549x-7062779$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[ ]$	$1$
402688.bg1	402688bg2	402688.bg	402688bg	$2$	$5$	$ 2^{8} \cdot 11^{2} \cdot 13 $	$ - 2^{9} \cdot 11^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$11440$	$48$	$1$	$5.680624215$	$1$		$2$	$1382400$	$1.466469$	$-85184/371293$	$1.11420$	$3.16950$	$1$	$[0, 1, 0, -887, -883291]$	$y^2=x^3+x^2-887x-883291$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[(3164, 177991)]$	$1$
402688.bn2	402688bn2	402688.bn	402688bn	$2$	$5$	$ 2^{8} \cdot 11^{2} \cdot 13 $	$ - 2^{15} \cdot 11^{6} \cdot 13^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.6.0.1	5B	$11440$	$48$	$1$	$2.488442407$	$1$		$2$	$2764800$	$1.813044$	$-85184/371293$	$1.11420$	$3.49175$	$1$	$[0, 1, 0, -3549, 7062779]$	$y^2=x^3+x^2-3549x+7062779$	5.6.0.a.1, 40.12.0.bp.2, 104.2.0.?, 260.12.0.?, 520.24.1.?, $\ldots$	$[(205, 3872)]$	$1$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (28 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.

Learn more

Refine search Advanced search options

Results (28 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.

Refine search