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 (28 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
7392.a4	7392b4	7392.a	7392b	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3 \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$2.326232654$	$1$		$3$	$2560$	$0.317388$	$36594368/79233$	$0.89420$	$3.00193$	$[0, -1, 0, 111, 705]$	$y^2=x^3-x^2+111x+705$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 44.12.0-4.c.1.2, 56.12.0-4.c.1.4, $\ldots$	$[(11, 56)]$
7392.j4	7392h4	7392.j	7392h	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3 \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$2560$	$0.317388$	$36594368/79233$	$0.89420$	$3.00193$	$[0, 1, 0, 111, -705]$	$y^2=x^3+x^2+111x-705$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 44.12.0-4.c.1.1, 56.12.0-4.c.1.4, $\ldots$	$[ ]$
14784.ba4	14784by1	14784.ba	14784by	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3 \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$3.910213203$	$1$		$1$	$2560$	$-0.029186$	$36594368/79233$	$0.89420$	$2.35205$	$[0, -1, 0, 28, -102]$	$y^2=x^3-x^2+28x-102$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.5, 88.12.0.?, $\ldots$	$[(37/2, 235/2)]$
14784.cg4	14784cf1	14784.cg	14784cf	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3 \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$4$	$2$	$1$	$2560$	$-0.029186$	$36594368/79233$	$0.89420$	$2.35205$	$[0, 1, 0, 28, 102]$	$y^2=x^3+x^2+28x+102$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.5, 88.12.0.?, $\ldots$	$[ ]$
22176.t4	22176o2	22176.t	22176o	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{7} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$20480$	$0.866693$	$36594368/79233$	$0.89420$	$3.33108$	$[0, 0, 0, 996, -20032]$	$y^2=x^3+996x-20032$	2.3.0.a.1, 4.12.0-4.c.1.2, 132.24.0.?, 168.24.0.?, 616.24.0.?, $\ldots$	$[ ]$
22176.u4	22176t2	22176.u	22176t	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{7} \cdot 7^{4} \cdot 11 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1848$	$48$	$0$	$1$	$1$		$3$	$20480$	$0.866693$	$36594368/79233$	$0.89420$	$3.33108$	$[0, 0, 0, 996, 20032]$	$y^2=x^3+996x+20032$	2.3.0.a.1, 4.12.0-4.c.1.1, 132.24.0.?, 168.24.0.?, 616.24.0.?, $\ldots$	$[ ]$
44352.bb4	44352dm1	44352.bb	44352dm	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{7} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1848$	$48$	$0$	$2.888696184$	$1$		$3$	$20480$	$0.520120$	$36594368/79233$	$0.89420$	$2.72660$	$[0, 0, 0, 249, -2504]$	$y^2=x^3+249x-2504$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 132.12.0.?, 168.24.0.?, $\ldots$	$[(44, 306)]$
44352.bt4	44352ex1	44352.bt	44352ex	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{7} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1848$	$48$	$0$	$3.065062148$	$1$		$3$	$20480$	$0.520120$	$36594368/79233$	$0.89420$	$2.72660$	$[0, 0, 0, 249, 2504]$	$y^2=x^3+249x+2504$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 132.12.0.?, 168.24.0.?, $\ldots$	$[(-4, 38)]$
51744.bg4	51744u2	51744.bg	51744u	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3 \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1848$	$48$	$0$	$7.112591022$	$1$		$1$	$122880$	$1.290342$	$36594368/79233$	$0.89420$	$3.53942$	$[0, -1, 0, 5423, 252673]$	$y^2=x^3-x^2+5423x+252673$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 132.12.0.?, $\ldots$	$[(-861/5, 19312/5)]$
51744.cl4	51744bn2	51744.cl	51744bn	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3 \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$1848$	$48$	$0$	$13.71261479$	$1$		$1$	$122880$	$1.290342$	$36594368/79233$	$0.89420$	$3.53942$	$[0, 1, 0, 5423, -252673]$	$y^2=x^3+x^2+5423x-252673$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 84.12.0.?, 132.12.0.?, $\ldots$	$[(744493/133, 535943400/133)]$
81312.i4	81312bg2	81312.i	81312bg	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3 \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$1848$	$48$	$0$	$1$	$1$		$3$	$307200$	$1.516335$	$36594368/79233$	$0.89420$	$3.63779$	$[0, -1, 0, 13391, -991967]$	$y^2=x^3-x^2+13391x-991967$	2.3.0.a.1, 4.12.0-4.c.1.1, 132.24.0.?, 168.24.0.?, 616.24.0.?, $\ldots$	$[ ]$
81312.be4	81312bn2	81312.be	81312bn	$4$	$4$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3 \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$307200$	$1.516335$	$36594368/79233$	$0.89420$	$3.63779$	$[0, 1, 0, 13391, 991967]$	$y^2=x^3+x^2+13391x+991967$	2.3.0.a.1, 4.12.0-4.c.1.2, 132.24.0.?, 168.24.0.?, 616.24.0.?, $\ldots$	$[ ]$
103488.bg4	103488gm1	103488.bg	103488gm	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3 \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1848$	$48$	$0$	$1$	$4$	$2$	$1$	$122880$	$0.943769$	$36594368/79233$	$0.89420$	$2.96680$	$[0, -1, 0, 1356, -32262]$	$y^2=x^3-x^2+1356x-32262$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 132.12.0.?, 168.24.0.?, $\ldots$	$[ ]$
103488.fi4	103488hw1	103488.fi	103488hw	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3 \cdot 7^{10} \cdot 11 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$1848$	$48$	$0$	$19.26254254$	$1$		$3$	$122880$	$0.943769$	$36594368/79233$	$0.89420$	$2.96680$	$[0, 1, 0, 1356, 32262]$	$y^2=x^3+x^2+1356x+32262$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 132.12.0.?, 168.24.0.?, $\ldots$	$[(17, 246), (-67/2, 573/2)]$
155232.w4	155232t3	155232.w	155232t	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3^{7} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$983040$	$1.839649$	$36594368/79233$	$0.89420$	$3.76558$	$[0, 0, 0, 48804, -6870976]$	$y^2=x^3+48804x-6870976$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 28.12.0-4.c.1.2, 88.12.0.?, $\ldots$	$[ ]$
155232.bn4	155232i3	155232.bn	155232i	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3^{7} \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1.165259917$	$1$		$7$	$983040$	$1.839649$	$36594368/79233$	$0.89420$	$3.76558$	$[0, 0, 0, 48804, 6870976]$	$y^2=x^3+48804x+6870976$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 28.12.0-4.c.1.1, 88.12.0.?, $\ldots$	$[(-70, 1764)]$
162624.dd4	162624dn1	162624.dd	162624dn	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3 \cdot 7^{4} \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$1848$	$48$	$0$	$6.057013020$	$1$		$1$	$307200$	$1.169762$	$36594368/79233$	$0.89420$	$3.08105$	$[0, -1, 0, 3348, 122322]$	$y^2=x^3-x^2+3348x+122322$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 132.12.0.?, 168.24.0.?, $\ldots$	$[(181/6, 80605/6)]$
162624.ia4	162624bf1	162624.ia	162624bf	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3 \cdot 7^{4} \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$1848$	$48$	$0$	$16.10811870$	$1$		$1$	$307200$	$1.169762$	$36594368/79233$	$0.89420$	$3.08105$	$[0, 1, 0, 3348, -122322]$	$y^2=x^3+x^2+3348x-122322$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 132.12.0.?, 168.24.0.?, $\ldots$	$[(9586729/99, 29747952350/99)]$
184800.bl4	184800de3	184800.bl	184800de	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$4.093842332$	$1$		$3$	$327680$	$1.122107$	$36594368/79233$	$0.89420$	$3.00142$	$[0, -1, 0, 2767, -93663]$	$y^2=x^3-x^2+2767x-93663$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 132.12.0.?, 168.12.0.?, $\ldots$	$[(811, 23128)]$
184800.fo4	184800y3	184800.fo	184800y	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$1$	$1$		$1$	$327680$	$1.122107$	$36594368/79233$	$0.89420$	$3.00142$	$[0, 1, 0, 2767, 93663]$	$y^2=x^3+x^2+2767x+93663$	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 132.12.0.?, 168.12.0.?, $\ldots$	$[ ]$
243936.cx4	243936cx3	243936.cx	243936cx	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3^{7} \cdot 7^{4} \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$4.020118135$	$1$		$3$	$2457600$	$2.065639$	$36594368/79233$	$0.89420$	$3.84700$	$[0, 0, 0, 120516, -26662592]$	$y^2=x^3+120516x-26662592$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 44.12.0-4.c.1.2, 56.12.0-4.c.1.6, $\ldots$	$[(8624, 801504)]$
243936.dg4	243936dg3	243936.dg	243936dg	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3^{7} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$1$		$1$	$2457600$	$2.065639$	$36594368/79233$	$0.89420$	$3.84700$	$[0, 0, 0, 120516, 26662592]$	$y^2=x^3+120516x+26662592$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 44.12.0-4.c.1.1, 56.12.0-4.c.1.6, $\ldots$	$[ ]$
310464.mz4	310464mz1	310464.mz	310464mz	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{7} \cdot 7^{10} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$4$	$2$	$1$	$983040$	$1.493074$	$36594368/79233$	$0.89420$	$3.23031$	$[0, 0, 0, 12201, 858872]$	$y^2=x^3+12201x+858872$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 56.12.0-4.c.1.2, 88.12.0.?, $\ldots$	$[ ]$
310464.op4	310464op1	310464.op	310464op	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{7} \cdot 7^{10} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$8.347875607$	$1$		$1$	$983040$	$1.493074$	$36594368/79233$	$0.89420$	$3.23031$	$[0, 0, 0, 12201, -858872]$	$y^2=x^3+12201x-858872$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 56.12.0-4.c.1.1, 88.12.0.?, $\ldots$	$[(2076/5, 106574/5)]$
369600.kf4	369600kf1	369600.kf	369600kf	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 11 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$9.201639773$	$1$		$5$	$327680$	$0.775533$	$36594368/79233$	$0.89420$	$2.51474$	$[0, -1, 0, 692, 11362]$	$y^2=x^3-x^2+692x+11362$	2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 132.12.0.?, 168.12.0.?, $\ldots$	$[(87, 850), (3, 116)]$
369600.mu4	369600mu1	369600.mu	369600mu	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3 \cdot 5^{6} \cdot 7^{4} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$9240$	$48$	$0$	$4.903487350$	$4$	$2$	$1$	$327680$	$0.775533$	$36594368/79233$	$0.89420$	$2.51474$	$[0, 1, 0, 692, -11362]$	$y^2=x^3+x^2+692x-11362$	2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 132.12.0.?, 168.12.0.?, $\ldots$	$[(517/3, 12700/3)]$
487872.dn4	487872dn1	487872.dn	487872dn	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3^{7} \cdot 7^{4} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1$	$4$	$2$	$1$	$2457600$	$1.719067$	$36594368/79233$	$0.89420$	$3.32589$	$[0, 0, 0, 30129, -3332824]$	$y^2=x^3+30129x-3332824$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 56.12.0-4.c.1.3, 88.12.0.?, $\ldots$	$[ ]$
487872.el4	487872el1	487872.el	487872el	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3^{7} \cdot 7^{4} \cdot 11^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1848$	$48$	$0$	$1.189414883$	$1$		$5$	$2457600$	$1.719067$	$36594368/79233$	$0.89420$	$3.32589$	$[0, 0, 0, 30129, 3332824]$	$y^2=x^3+30129x+3332824$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 56.12.0-4.c.1.3, 88.12.0.?, $\ldots$	$[(44, 2178)]$

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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

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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 (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