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 (33 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	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
632.a1	632a1	632.a	632a	$1$	$1$	$ 2^{3} \cdot 79 $	$ 2^{10} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$0.329352174$	$1$		$4$	$64$	$-0.337239$	$470596/79$	$1.06719$	$3.10026$	$[0, 1, 0, -16, 16]$	$y^2=x^3+x^2-16x+16$	316.2.0.?	$[(0, 4)]$
1264.b1	1264a1	1264.b	1264a	$1$	$1$	$ 2^{4} \cdot 79 $	$ 2^{10} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$0.483463932$	$1$		$4$	$128$	$-0.337239$	$470596/79$	$1.06719$	$2.79937$	$[0, -1, 0, -16, -16]$	$y^2=x^3-x^2-16x-16$	316.2.0.?	$[(-2, 2)]$
5056.g1	5056g1	5056.g	5056g	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{16} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$0.425619931$	$1$		$14$	$1024$	$0.009334$	$470596/79$	$1.06719$	$2.83199$	$[0, -1, 0, -65, 193]$	$y^2=x^3-x^2-65x+193$	316.2.0.?	$[(9, 16), (-7, 16)]$
5056.p1	5056l1	5056.p	5056l	$1$	$1$	$ 2^{6} \cdot 79 $	$ 2^{16} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$1024$	$0.009334$	$470596/79$	$1.06719$	$2.83199$	$[0, 1, 0, -65, -193]$	$y^2=x^3+x^2-65x-193$	316.2.0.?	$[]$
5688.b1	5688c1	5688.b	5688c	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 79 $	$ 2^{10} \cdot 3^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1.282183592$	$1$		$4$	$1920$	$0.212067$	$470596/79$	$1.06719$	$3.07478$	$[0, 0, 0, -147, -578]$	$y^2=x^3-147x-578$	316.2.0.?	$[(-9, 4)]$
11376.n1	11376c1	11376.n	11376c	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 79 $	$ 2^{10} \cdot 3^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$3840$	$0.212067$	$470596/79$	$1.06719$	$2.84657$	$[0, 0, 0, -147, 578]$	$y^2=x^3-147x+578$	316.2.0.?	$[]$
15800.b1	15800b1	15800.b	15800b	$1$	$1$	$ 2^{3} \cdot 5^{2} \cdot 79 $	$ 2^{10} \cdot 5^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$8960$	$0.467480$	$470596/79$	$1.06719$	$3.06688$	$[0, -1, 0, -408, 2812]$	$y^2=x^3-x^2-408x+2812$	316.2.0.?	$[]$
30968.c1	30968f1	30968.c	30968f	$1$	$1$	$ 2^{3} \cdot 7^{2} \cdot 79 $	$ 2^{10} \cdot 7^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$14976$	$0.635715$	$470596/79$	$1.06719$	$3.06253$	$[0, -1, 0, -800, -7076]$	$y^2=x^3-x^2-800x-7076$	316.2.0.?	$[]$
31600.q1	31600b1	31600.q	31600b	$1$	$1$	$ 2^{4} \cdot 5^{2} \cdot 79 $	$ 2^{10} \cdot 5^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$2.032196740$	$1$		$4$	$17920$	$0.467480$	$470596/79$	$1.06719$	$2.86170$	$[0, 1, 0, -408, -2812]$	$y^2=x^3+x^2-408x-2812$	316.2.0.?	$[(-8, 2)]$
45504.w1	45504x1	45504.w	45504x	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 79 $	$ 2^{16} \cdot 3^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1.185310975$	$1$		$4$	$30720$	$0.558640$	$470596/79$	$1.06719$	$2.86640$	$[0, 0, 0, -588, -4624]$	$y^2=x^3-588x-4624$	316.2.0.?	$[(-10, 16)]$
45504.z1	45504bk1	45504.z	45504bk	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 79 $	$ 2^{16} \cdot 3^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$2.523104276$	$1$		$2$	$30720$	$0.558640$	$470596/79$	$1.06719$	$2.86640$	$[0, 0, 0, -588, 4624]$	$y^2=x^3-588x+4624$	316.2.0.?	$[(0, 68)]$
49928.a1	49928a1	49928.a	49928a	$1$	$1$	$ 2^{3} \cdot 79^{2} $	$ 2^{10} \cdot 79^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$2.909163756$	$1$		$0$	$399360$	$1.847485$	$470596/79$	$1.06719$	$4.27144$	$[0, -1, 0, -101936, -10520708]$	$y^2=x^3-x^2-101936x-10520708$	316.2.0.?	$[(-7594/7, 424388/7)]$
61936.u1	61936a1	61936.u	61936a	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 79 $	$ 2^{10} \cdot 7^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$29952$	$0.635715$	$470596/79$	$1.06719$	$2.87014$	$[0, 1, 0, -800, 7076]$	$y^2=x^3+x^2-800x+7076$	316.2.0.?	$[]$
76472.b1	76472a1	76472.b	76472a	$1$	$1$	$ 2^{3} \cdot 11^{2} \cdot 79 $	$ 2^{10} \cdot 11^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$81920$	$0.861709$	$470596/79$	$1.06719$	$3.05750$	$[0, 1, 0, -1976, -29152]$	$y^2=x^3+x^2-1976x-29152$	316.2.0.?	$[]$
99856.m1	99856a1	99856.m	99856a	$1$	$1$	$ 2^{4} \cdot 79^{2} $	$ 2^{10} \cdot 79^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$798720$	$1.847485$	$470596/79$	$1.06719$	$4.01424$	$[0, 1, 0, -101936, 10520708]$	$y^2=x^3+x^2-101936x+10520708$	316.2.0.?	$[]$
106808.k1	106808d1	106808.k	106808d	$1$	$1$	$ 2^{3} \cdot 13^{2} \cdot 79 $	$ 2^{10} \cdot 13^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$149760$	$0.945235$	$470596/79$	$1.06719$	$3.05584$	$[0, 1, 0, -2760, 46112]$	$y^2=x^3+x^2-2760x+46112$	316.2.0.?	$[]$
126400.n1	126400bo1	126400.n	126400bo	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 79 $	$ 2^{16} \cdot 5^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$143360$	$0.814054$	$470596/79$	$1.06719$	$2.87802$	$[0, -1, 0, -1633, -20863]$	$y^2=x^3-x^2-1633x-20863$	316.2.0.?	$[]$
126400.cg1	126400u1	126400.cg	126400u	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 79 $	$ 2^{16} \cdot 5^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$143360$	$0.814054$	$470596/79$	$1.06719$	$2.87802$	$[0, 1, 0, -1633, 20863]$	$y^2=x^3+x^2-1633x+20863$	316.2.0.?	$[]$
142200.bx1	142200p1	142200.bx	142200p	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 79 $	$ 2^{10} \cdot 3^{6} \cdot 5^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$268800$	$1.016787$	$470596/79$	$1.06719$	$3.05449$	$[0, 0, 0, -3675, -72250]$	$y^2=x^3-3675x-72250$	316.2.0.?	$[]$
152944.f1	152944w1	152944.f	152944w	$1$	$1$	$ 2^{4} \cdot 11^{2} \cdot 79 $	$ 2^{10} \cdot 11^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$0.954851830$	$1$		$4$	$163840$	$0.861709$	$470596/79$	$1.06719$	$2.87997$	$[0, -1, 0, -1976, 29152]$	$y^2=x^3-x^2-1976x+29152$	316.2.0.?	$[(-18, 242)]$
182648.e1	182648b1	182648.e	182648b	$1$	$1$	$ 2^{3} \cdot 17^{2} \cdot 79 $	$ 2^{10} \cdot 17^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$266240$	$1.079367$	$470596/79$	$1.06719$	$3.05337$	$[0, -1, 0, -4720, 106748]$	$y^2=x^3-x^2-4720x+106748$	316.2.0.?	$[]$
213616.g1	213616y1	213616.g	213616y	$1$	$1$	$ 2^{4} \cdot 13^{2} \cdot 79 $	$ 2^{10} \cdot 13^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$3.025719381$	$1$		$2$	$299520$	$0.945235$	$470596/79$	$1.06719$	$2.88324$	$[0, -1, 0, -2760, -46112]$	$y^2=x^3-x^2-2760x-46112$	316.2.0.?	$[(-26, 86)]$
228152.b1	228152g1	228152.b	228152g	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 79 $	$ 2^{10} \cdot 19^{6} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$3.660126817$	$1$		$6$	$456192$	$1.134981$	$470596/79$	$1.06719$	$3.05240$	$[0, -1, 0, -5896, -144868]$	$y^2=x^3-x^2-5896x-144868$	316.2.0.?	$[(146, 1444), (-46, 164)]$
247744.p1	247744p1	247744.p	247744p	$1$	$1$	$ 2^{6} \cdot 7^{2} \cdot 79 $	$ 2^{16} \cdot 7^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$3.828377837$	$1$		$2$	$239616$	$0.982289$	$470596/79$	$1.06719$	$2.88463$	$[0, -1, 0, -3201, 59809]$	$y^2=x^3-x^2-3201x+59809$	316.2.0.?	$[(-57, 232)]$
247744.bw1	247744bw1	247744.bw	247744bw	$1$	$1$	$ 2^{6} \cdot 7^{2} \cdot 79 $	$ 2^{16} \cdot 7^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$2.860550235$	$1$		$2$	$239616$	$0.982289$	$470596/79$	$1.06719$	$2.88463$	$[0, 1, 0, -3201, -59809]$	$y^2=x^3+x^2-3201x-59809$	316.2.0.?	$[(67, 176)]$
278712.l1	278712l1	278712.l	278712l	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 79 $	$ 2^{10} \cdot 3^{6} \cdot 7^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$449280$	$1.185022$	$470596/79$	$1.06719$	$3.05157$	$[0, 0, 0, -7203, 198254]$	$y^2=x^3-7203x+198254$	316.2.0.?	$[]$
284400.e1	284400e1	284400.e	284400e	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 79 $	$ 2^{10} \cdot 3^{6} \cdot 5^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$537600$	$1.016787$	$470596/79$	$1.06719$	$2.88590$	$[0, 0, 0, -3675, 72250]$	$y^2=x^3-3675x+72250$	316.2.0.?	$[]$
334328.g1	334328g1	334328.g	334328g	$1$	$1$	$ 2^{3} \cdot 23^{2} \cdot 79 $	$ 2^{10} \cdot 23^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$6.549126281$	$1$		$0$	$760320$	$1.230509$	$470596/79$	$1.06719$	$3.05083$	$[0, 1, 0, -8640, -263344]$	$y^2=x^3+x^2-8640x-263344$	316.2.0.?	$[(10861/10, 302059/10)]$
365296.bf1	365296bf1	365296.bf	365296bf	$1$	$1$	$ 2^{4} \cdot 17^{2} \cdot 79 $	$ 2^{10} \cdot 17^{6} \cdot 79 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$7.279535950$	$1$		$4$	$532480$	$1.079367$	$470596/79$	$1.06719$	$2.88813$	$[0, 1, 0, -4720, -106748]$	$y^2=x^3+x^2-4720x-106748$	316.2.0.?	$[(96, 578), (-296/3, 3194/3)]$
399424.i1	399424i1	399424.i	399424i	$1$	$1$	$ 2^{6} \cdot 79^{2} $	$ 2^{16} \cdot 79^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$5.760694827$	$1$		$0$	$6389760$	$2.194057$	$470596/79$	$1.06719$	$3.90523$	$[0, -1, 0, -407745, 84573409]$	$y^2=x^3-x^2-407745x+84573409$	316.2.0.?	$[(-30425/7, 3395104/7)]$
399424.bi1	399424bi1	399424.bi	399424bi	$1$	$1$	$ 2^{6} \cdot 79^{2} $	$ 2^{16} \cdot 79^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$1$	$1$		$0$	$6389760$	$2.194057$	$470596/79$	$1.06719$	$3.90523$	$[0, 1, 0, -407745, -84573409]$	$y^2=x^3+x^2-407745x-84573409$	316.2.0.?	$[]$
449352.f1	449352f1	449352.f	449352f	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 79^{2} $	$ 2^{10} \cdot 3^{6} \cdot 79^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$0.686899503$	$9$	$3$	$4$	$11980800$	$2.396790$	$470596/79$	$1.06719$	$4.05680$	$[0, 0, 0, -917427, 284976542]$	$y^2=x^3-917427x+284976542$	316.2.0.?	$[(-553, 24964)]$
456304.ba1	456304ba1	456304.ba	456304ba	$1$	$1$	$ 2^{4} \cdot 19^{2} \cdot 79 $	$ 2^{10} \cdot 19^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$316$	$2$	$0$	$2.747006405$	$1$		$2$	$912384$	$1.134981$	$470596/79$	$1.06719$	$2.89004$	$[0, 1, 0, -5896, 144868]$	$y^2=x^3+x^2-5896x+144868$	316.2.0.?	$[(576, 13718)]$

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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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