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 (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
6240.a1	6240b3	6240.a	6240b	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$520$	$48$	$0$	$0.628717566$	$1$		$7$	$3072$	$0.459747$	$428320044872/73125$	$0.93037$	$3.77875$	$[0, -1, 0, -1256, 17556]$	$y^2=x^3-x^2-1256x+17556$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 40.24.0-40.bb.1.14, 52.12.0-4.c.1.2, $\ldots$	$[(20, 6)]$
6240.x1	6240k2	6240.x	6240k	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{4} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$520$	$48$	$0$	$1$	$4$	$2$	$1$	$3072$	$0.459747$	$428320044872/73125$	$0.93037$	$3.77875$	$[0, 1, 0, -1256, -17556]$	$y^2=x^3+x^2-1256x-17556$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 40.24.0-40.bb.1.6, 52.12.0-4.c.1.1, $\ldots$	$[]$
12480.bp1	12480ci3	12480.bp	12480ci	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 5^{4} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$520$	$48$	$0$	$1$	$1$		$1$	$12288$	$0.806320$	$428320044872/73125$	$0.93037$	$3.94199$	$[0, -1, 0, -5025, -135423]$	$y^2=x^3-x^2-5025x-135423$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.bb.1.10, 104.24.0.?, 520.48.0.?	$[]$
12480.cp1	12480dh4	12480.cp	12480dh	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 5^{4} \cdot 13 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$520$	$48$	$0$	$1.991073726$	$1$		$11$	$12288$	$0.806320$	$428320044872/73125$	$0.93037$	$3.94199$	$[0, 1, 0, -5025, 135423]$	$y^2=x^3+x^2-5025x+135423$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.bb.1.2, 104.24.0.?, 520.48.0.?	$[(42, 15)]$
18720.x1	18720bn2	18720.x	18720bn	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 5^{4} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$24576$	$1.009052$	$428320044872/73125$	$0.93037$	$4.02681$	$[0, 0, 0, -11307, -462706]$	$y^2=x^3-11307x-462706$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[]$
18720.br1	18720bm3	18720.br	18720bm	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 5^{4} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$24576$	$1.009052$	$428320044872/73125$	$0.93037$	$4.02681$	$[0, 0, 0, -11307, 462706]$	$y^2=x^3-11307x+462706$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[]$
31200.a1	31200bq4	31200.a	31200bq	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$520$	$48$	$0$	$5.413205463$	$1$		$1$	$73728$	$1.264465$	$428320044872/73125$	$0.93037$	$4.12421$	$[0, -1, 0, -31408, -2131688]$	$y^2=x^3-x^2-31408x-2131688$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.bb.1.13, 104.24.0.?, $\ldots$	$[(-911/3, 316/3)]$
31200.cj1	31200cg4	31200.cj	31200cg	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{10} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$520$	$48$	$0$	$1$	$1$		$1$	$73728$	$1.264465$	$428320044872/73125$	$0.93037$	$4.12421$	$[0, 1, 0, -31408, 2131688]$	$y^2=x^3+x^2-31408x+2131688$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.bb.1.5, 104.24.0.?, $\ldots$	$[]$
37440.c1	37440es4	37440.c	37440es	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 13 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$11.43081973$	$1$		$9$	$98304$	$1.355627$	$428320044872/73125$	$0.93037$	$4.15669$	$[0, 0, 0, -45228, -3701648]$	$y^2=x^3-45228x-3701648$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[(-123, 23), (276, 2200)]$
37440.cu1	37440ep4	37440.cu	37440ep	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 $	$ 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$98304$	$1.355627$	$428320044872/73125$	$0.93037$	$4.15669$	$[0, 0, 0, -45228, 3701648]$	$y^2=x^3-45228x+3701648$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[]$
62400.ec1	62400ek4	62400.ec	62400ek	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 5^{10} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$520$	$48$	$0$	$1$	$1$		$1$	$294912$	$1.611040$	$428320044872/73125$	$0.93037$	$4.24197$	$[0, -1, 0, -125633, 17179137]$	$y^2=x^3-x^2-125633x+17179137$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.2, 40.24.0-40.bb.1.9, $\ldots$	$[]$
62400.ef1	62400gu4	62400.ef	62400gu	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{2} \cdot 5^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$520$	$48$	$0$	$2.666311988$	$1$		$5$	$294912$	$1.611040$	$428320044872/73125$	$0.93037$	$4.24197$	$[0, 1, 0, -125633, -17179137]$	$y^2=x^3+x^2-125633x-17179137$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.1, 40.24.0-40.bb.1.1, $\ldots$	$[(-203, 12)]$
81120.bb1	81120bl4	81120.bb	81120bl	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{9} \cdot 3^{2} \cdot 5^{4} \cdot 13^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$520$	$48$	$0$	$3.648149229$	$1$		$5$	$516096$	$1.742222$	$428320044872/73125$	$0.93037$	$4.28278$	$[0, -1, 0, -212320, 37721332]$	$y^2=x^3-x^2-212320x+37721332$	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.bb.1.15, 104.24.0.?, 520.48.0.?	$[(-356, 8250)]$
81120.bq1	81120cc4	81120.bq	81120cc	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{9} \cdot 3^{2} \cdot 5^{4} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$520$	$48$	$0$	$1$	$1$		$1$	$516096$	$1.742222$	$428320044872/73125$	$0.93037$	$4.28278$	$[0, 1, 0, -212320, -37721332]$	$y^2=x^3+x^2-212320x-37721332$	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.bb.1.7, 104.24.0.?, 520.48.0.?	$[]$
93600.h1	93600bx4	93600.h	93600bx	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 5^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$3.904407499$	$1$		$3$	$589824$	$1.813772$	$428320044872/73125$	$0.93037$	$4.30424$	$[0, 0, 0, -282675, 57838250]$	$y^2=x^3-282675x+57838250$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[(346, 1206)]$
93600.ey1	93600bw4	93600.ey	93600bw	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{9} \cdot 3^{8} \cdot 5^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$11.26939109$	$1$		$1$	$589824$	$1.813772$	$428320044872/73125$	$0.93037$	$4.30424$	$[0, 0, 0, -282675, -57838250]$	$y^2=x^3-282675x-57838250$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[(-971071/56, 7535583/56)]$
162240.h1	162240dj4	162240.h	162240dj	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{15} \cdot 3^{2} \cdot 5^{4} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$520$	$48$	$0$	$1$	$1$		$1$	$2064384$	$2.088795$	$428320044872/73125$	$0.93037$	$4.38199$	$[0, -1, 0, -849281, -300921375]$	$y^2=x^3-x^2-849281x-300921375$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 40.24.0-40.bb.1.11, 52.12.0-4.c.1.1, $\ldots$	$[]$
162240.fz1	162240bu3	162240.fz	162240bu	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ 2^{15} \cdot 3^{2} \cdot 5^{4} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$520$	$48$	$0$	$6.516660376$	$1$		$1$	$2064384$	$2.088795$	$428320044872/73125$	$0.93037$	$4.38199$	$[0, 1, 0, -849281, 300921375]$	$y^2=x^3+x^2-849281x+300921375$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 40.24.0-40.bb.1.3, 52.12.0-4.c.1.2, $\ldots$	$[(28813/7, 781500/7)]$
187200.bq1	187200cv3	187200.bq	187200cv	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{8} \cdot 5^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$5.035816449$	$1$		$3$	$2359296$	$2.160347$	$428320044872/73125$	$0.93037$	$4.40107$	$[0, 0, 0, -1130700, 462706000]$	$y^2=x^3-1130700x+462706000$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 40.12.0.bb.1, 60.12.0-4.c.1.1, $\ldots$	$[(1196, 28656)]$
187200.ow1	187200ga4	187200.ow	187200ga	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ 2^{15} \cdot 3^{8} \cdot 5^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1.838902589$	$4$	$2$	$7$	$2359296$	$2.160347$	$428320044872/73125$	$0.93037$	$4.40107$	$[0, 0, 0, -1130700, -462706000]$	$y^2=x^3-1130700x-462706000$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 40.12.0.bb.1, 60.12.0-4.c.1.2, $\ldots$	$[(-610, 200)]$
243360.g1	243360g2	243360.g	243360g	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{9} \cdot 3^{8} \cdot 5^{4} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$4128768$	$2.291527$	$428320044872/73125$	$0.93037$	$4.43489$	$[0, 0, 0, -1910883, 1016565082]$	$y^2=x^3-1910883x+1016565082$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[]$
243360.cl1	243360cl4	243360.cl	243360cl	$4$	$4$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{9} \cdot 3^{8} \cdot 5^{4} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$4128768$	$2.291527$	$428320044872/73125$	$0.93037$	$4.43489$	$[0, 0, 0, -1910883, -1016565082]$	$y^2=x^3-1910883x-1016565082$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[]$
305760.dn1	305760dn2	305760.dn	305760dn	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{4} \cdot 7^{6} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3640$	$48$	$0$	$1$	$1$		$1$	$884736$	$1.432701$	$428320044872/73125$	$0.93037$	$3.53879$	$[0, -1, 0, -61560, 5898600]$	$y^2=x^3-x^2-61560x+5898600$	2.3.0.a.1, 4.6.0.c.1, 40.12.0.bb.1, 56.12.0-4.c.1.2, 104.12.0.?, $\ldots$	$[]$
305760.gf1	305760gf4	305760.gf	305760gf	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 $	$ 2^{9} \cdot 3^{2} \cdot 5^{4} \cdot 7^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3640$	$48$	$0$	$4.167376782$	$1$		$3$	$884736$	$1.432701$	$428320044872/73125$	$0.93037$	$3.53879$	$[0, 1, 0, -61560, -5898600]$	$y^2=x^3+x^2-61560x-5898600$	2.3.0.a.1, 4.6.0.c.1, 40.12.0.bb.1, 56.12.0-4.c.1.1, 104.12.0.?, $\ldots$	$[(639, 14700)]$
405600.df1	405600df4	405600.df	405600df	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{9} \cdot 3^{2} \cdot 5^{10} \cdot 13^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.13	2B	$520$	$48$	$0$	$21.93201351$	$1$		$1$	$12386304$	$2.546940$	$428320044872/73125$	$0.93037$	$4.49680$	$[0, -1, 0, -5308008, -4704550488]$	$y^2=x^3-x^2-5308008x-4704550488$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.6, 20.12.0-4.c.1.1, 40.24.0-40.bb.1.16, $\ldots$	$[(-13721386451/3213, 27603300798926/3213)]$
405600.dz1	405600dz2	405600.dz	405600dz	$4$	$4$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ 2^{9} \cdot 3^{2} \cdot 5^{10} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.13	2B	$520$	$48$	$0$	$1$	$1$		$1$	$12386304$	$2.546940$	$428320044872/73125$	$0.93037$	$4.49680$	$[0, 1, 0, -5308008, 4704550488]$	$y^2=x^3+x^2-5308008x+4704550488$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.6, 20.12.0-4.c.1.2, 40.24.0-40.bb.1.8, $\ldots$	$[]$
486720.iv1	486720iv3	486720.iv	486720iv	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$		$1$	$16515072$	$2.638100$	$428320044872/73125$	$0.93037$	$4.51773$	$[0, 0, 0, -7643532, 8132520656]$	$y^2=x^3-7643532x+8132520656$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[]$
486720.ql1	486720ql4	486720.ql	486720ql	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ 2^{15} \cdot 3^{8} \cdot 5^{4} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$4$	$2$	$1$	$16515072$	$2.638100$	$428320044872/73125$	$0.93037$	$4.51773$	$[0, 0, 0, -7643532, -8132520656]$	$y^2=x^3-7643532x-8132520656$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0.bb.1, 104.12.0.?, $\ldots$	$[]$

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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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