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
6930.e1	6930b2	6930.e	6930b	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{4} \cdot 3^{3} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.338264876$	$1$	$10$	$3072$	$0.428847$	$8493409990827/474320$	$0.92219$	$3.73899$	$[1, -1, 0, -1275, 17845]$	$y^2+xy=x^3-x^2-1275x+17845$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(18, 13)]$
6930.bh1	6930u2	6930.bh	6930u	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{4} \cdot 3^{9} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$0$	$9216$	$0.978153$	$8493409990827/474320$	$0.92219$	$4.48435$	$[1, -1, 1, -11477, -470339]$	$y^2+xy+y=x^3-x^2-11477x-470339$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
34650.d1	34650a2	34650.d	34650a	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{4} \cdot 3^{9} \cdot 5^{7} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$2.152352394$	$1$	$4$	$221184$	$1.782873$	$8493409990827/474320$	$0.92219$	$4.71771$	$[1, -1, 0, -286917, -59079259]$	$y^2+xy=x^3-x^2-286917x-59079259$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(-310, 199)]$
34650.dj1	34650cn2	34650.dj	34650cn	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{4} \cdot 3^{3} \cdot 5^{7} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$0.293445897$	$1$	$10$	$73728$	$1.233566$	$8493409990827/474320$	$0.92219$	$4.08711$	$[1, -1, 1, -31880, 2198747]$	$y^2+xy+y=x^3-x^2-31880x+2198747$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(99, 25)]$
48510.bx1	48510k2	48510.bx	48510k	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 3^{3} \cdot 5 \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$0$	$147456$	$1.401802$	$8493409990827/474320$	$0.92219$	$4.14676$	$[1, -1, 0, -62484, -5995872]$	$y^2+xy=x^3-x^2-62484x-5995872$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
48510.cl1	48510cb2	48510.cl	48510cb	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 3^{9} \cdot 5 \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.198738248$	$1$	$6$	$442368$	$1.951109$	$8493409990827/474320$	$0.92219$	$4.75770$	$[1, -1, 1, -562358, 162450901]$	$y^2+xy+y=x^3-x^2-562358x+162450901$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(443, 121)]$
55440.h1	55440bv2	55440.h	55440bv	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{3} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$73728$	$1.121994$	$8493409990827/474320$	$0.92219$	$3.78868$	$[0, 0, 0, -20403, -1121678]$	$y^2=x^3-20403x-1121678$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
55440.dn1	55440ci2	55440.dn	55440ci	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{9} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$221184$	$1.671301$	$8493409990827/474320$	$0.92219$	$4.39214$	$[0, 0, 0, -183627, 30285306]$	$y^2=x^3-183627x+30285306$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
76230.br1	76230h2	76230.br	76230h	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{4} \cdot 3^{9} \cdot 5 \cdot 7^{2} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.816664501$	$1$	$6$	$1105920$	$2.177101$	$8493409990827/474320$	$0.92219$	$4.80765$	$[1, -1, 0, -1388679, 630186893]$	$y^2+xy=x^3-x^2-1388679x+630186893$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(674, -95)]$
76230.dd1	76230cs2	76230.dd	76230cs	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{4} \cdot 3^{3} \cdot 5 \cdot 7^{2} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$2.513366595$	$1$	$2$	$368640$	$1.627794$	$8493409990827/474320$	$0.92219$	$4.22128$	$[1, -1, 1, -154298, -23288823]$	$y^2+xy+y=x^3-x^2-154298x-23288823$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(531, 6389)]$
221760.bf1	221760hm2	221760.bf	221760hm	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{22} \cdot 3^{9} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$1769472$	$2.017876$	$8493409990827/474320$	$0.92219$	$4.23536$	$[0, 0, 0, -734508, 242282448]$	$y^2=x^3-734508x+242282448$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
221760.gd1	221760nn2	221760.gd	221760nn	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{22} \cdot 3^{9} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$6.656315567$	$1$	$3$	$1769472$	$2.017876$	$8493409990827/474320$	$0.92219$	$4.23536$	$[0, 0, 0, -734508, -242282448]$	$y^2=x^3-734508x-242282448$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(213942, 98955648)]$
221760.ji1	221760gh2	221760.ji	221760gh	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{22} \cdot 3^{3} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$589824$	$1.468569$	$8493409990827/474320$	$0.92219$	$3.69985$	$[0, 0, 0, -81612, -8973424]$	$y^2=x^3-81612x-8973424$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
221760.lw1	221760mw2	221760.lw	221760mw	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{22} \cdot 3^{3} \cdot 5 \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.428797934$	$1$	$3$	$589824$	$1.468569$	$8493409990827/474320$	$0.92219$	$3.69985$	$[0, 0, 0, -81612, 8973424]$	$y^2=x^3-81612x+8973424$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(110, 1152)]$
242550.bg1	242550bg2	242550.bg	242550bg	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 3^{9} \cdot 5^{7} \cdot 7^{8} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.633816023$	$1$	$20$	$10616832$	$2.755829$	$8493409990827/474320$	$0.92219$	$4.91895$	$[1, -1, 0, -14058942, 20292303716]$	$y^2+xy=x^3-x^2-14058942x+20292303716$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(2249, 5613), (2524, 28438)]$
242550.mn1	242550mn2	242550.mn	242550mn	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ 2^{4} \cdot 3^{3} \cdot 5^{7} \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$0$	$3538944$	$2.206520$	$8493409990827/474320$	$0.92219$	$4.38732$	$[1, -1, 1, -1562105, -751046103]$	$y^2+xy+y=x^3-x^2-1562105x-751046103$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
277200.jx1	277200jx2	277200.jx	277200jx	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{3} \cdot 5^{7} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$3.157353765$	$1$	$3$	$1769472$	$1.926714$	$8493409990827/474320$	$0.92219$	$4.07266$	$[0, 0, 0, -510075, -140209750]$	$y^2=x^3-510075x-140209750$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(1130, 26950)]$
277200.mv1	277200mv2	277200.mv	277200mv	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{9} \cdot 5^{7} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$5308416$	$2.476021$	$8493409990827/474320$	$0.92219$	$4.59862$	$[0, 0, 0, -4590675, 3785663250]$	$y^2=x^3-4590675x+3785663250$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
381150.fl1	381150fl2	381150.fl	381150fl	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ 2^{4} \cdot 3^{3} \cdot 5^{7} \cdot 7^{2} \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1.665634704$	$1$	$6$	$8847360$	$2.432514$	$8493409990827/474320$	$0.92219$	$4.44404$	$[1, -1, 0, -3857442, -2914960284]$	$y^2+xy=x^3-x^2-3857442x-2914960284$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[(-1136, 918)]$
381150.nz1	381150nz2	381150.nz	381150nz	$2$	$2$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} $	$ 2^{4} \cdot 3^{9} \cdot 5^{7} \cdot 7^{2} \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$0$	$26542080$	$2.981819$	$8493409990827/474320$	$0.92219$	$4.95697$	$[1, -1, 1, -34716980, 78738644647]$	$y^2+xy+y=x^3-x^2-34716980x+78738644647$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
388080.gb1	388080gb2	388080.gb	388080gb	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{16} \cdot 3^{9} \cdot 5 \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$10616832$	$2.644257$	$8493409990827/474320$	$0.92219$	$4.63526$	$[0, 0, 0, -8997723, -10387859958]$	$y^2=x^3-8997723x-10387859958$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$
388080.kf1	388080kf2	388080.kf	388080kf	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{16} \cdot 3^{3} \cdot 5 \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$4620$	$12$	$0$	$1$	$1$	$1$	$3538944$	$2.094948$	$8493409990827/474320$	$0.92219$	$4.12305$	$[0, 0, 0, -999747, 384735554]$	$y^2=x^3-999747x+384735554$	2.3.0.a.1, 60.6.0.a.1, 924.6.0.?, 1540.6.0.?, 4620.12.0.?	$[ ]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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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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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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