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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
1950.f2	1950m1	1950.f	1950m	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$312$	$16$	$0$	$1$	$1$	$2$	$3240$	$0.963123$	$7604375/2047032$	$1.24246$	$4.60162$	$[1, 0, 1, 299, -42952]$	$y^2+xy+y=x^3+299x-42952$	3.8.0-3.a.1.2, 312.16.0.?	$[ ]$
1950.t2	1950o1	1950.t	1950o	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$648$	$0.158404$	$7604375/2047032$	$1.24246$	$3.32692$	$[1, 1, 1, 12, -339]$	$y^2+xy+y=x^3+x^2+12x-339$	3.4.0.a.1, 15.8.0-3.a.1.2, 312.8.0.?, 1560.16.0.?	$[ ]$
5850.y2	5850k1	5850.y	5850k	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{15} \cdot 5^{2} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$5184$	$0.707710$	$7604375/2047032$	$1.24246$	$3.66547$	$[1, -1, 0, 108, 9256]$	$y^2+xy=x^3-x^2+108x+9256$	3.4.0.a.1, 15.8.0-3.a.1.1, 312.8.0.?, 1560.16.0.?	$[ ]$
5850.be2	5850cc1	5850.be	5850cc	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{15} \cdot 5^{8} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$312$	$16$	$0$	$1.112926632$	$1$	$4$	$25920$	$1.512430$	$7604375/2047032$	$1.24246$	$4.77873$	$[1, -1, 1, 2695, 1159697]$	$y^2+xy+y=x^3-x^2+2695x+1159697$	3.8.0-3.a.1.1, 312.16.0.?	$[(-75, 766)]$
15600.bj2	15600bx1	15600.bj	15600bx	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{15} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$	$0$	$77760$	$1.656271$	$7604375/2047032$	$1.24246$	$4.47205$	$[0, -1, 0, 4792, 2748912]$	$y^2=x^3-x^2+4792x+2748912$	3.4.0.a.1, 12.8.0-3.a.1.1, 312.16.0.?	$[ ]$
15600.br2	15600cg1	15600.br	15600cg	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{15} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$0.178073772$	$1$	$8$	$15552$	$0.851552$	$7604375/2047032$	$1.24246$	$3.47188$	$[0, 1, 0, 192, 22068]$	$y^2=x^3+x^2+192x+22068$	3.4.0.a.1, 60.8.0-3.a.1.2, 312.8.0.?, 1560.16.0.?	$[(-6, 144)]$
25350.e2	25350h1	25350.e	25350h	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3^{9} \cdot 5^{2} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$2.209525746$	$1$	$2$	$108864$	$1.440880$	$7604375/2047032$	$1.24246$	$4.00305$	$[1, 1, 0, 2025, -754515]$	$y^2+xy=x^3+x^2+2025x-754515$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[(161, 1863)]$
25350.dn2	25350dl1	25350.dn	25350dl	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3^{9} \cdot 5^{8} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$	$0$	$544320$	$2.245598$	$7604375/2047032$	$1.24246$	$4.95533$	$[1, 0, 0, 50612, -94415608]$	$y^2+xy=x^3+50612x-94415608$	3.4.0.a.1, 24.8.0-3.a.1.5, 39.8.0-3.a.1.1, 312.16.0.?	$[ ]$
46800.l2	46800dl1	46800.l	46800dl	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{15} \cdot 3^{15} \cdot 5^{2} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$2.001077558$	$1$	$2$	$124416$	$1.400858$	$7604375/2047032$	$1.24246$	$3.73016$	$[0, 0, 0, 1725, -594110]$	$y^2=x^3+1725x-594110$	3.4.0.a.1, 60.8.0-3.a.1.1, 312.8.0.?, 1560.16.0.?	$[(206, 2916)]$
46800.fj2	46800fn1	46800.fj	46800fn	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{15} \cdot 3^{15} \cdot 5^{8} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$7.381798666$	$1$	$0$	$622080$	$2.205578$	$7604375/2047032$	$1.24246$	$4.62815$	$[0, 0, 0, 43125, -74263750]$	$y^2=x^3+43125x-74263750$	3.4.0.a.1, 12.8.0-3.a.1.2, 312.16.0.?	$[(8221/3, 728144/3)]$
62400.j2	62400bm1	62400.j	62400bm	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$	$0$	$622080$	$2.002846$	$7604375/2047032$	$1.24246$	$4.28722$	$[0, -1, 0, 19167, -22010463]$	$y^2=x^3-x^2+19167x-22010463$	3.4.0.a.1, 24.8.0-3.a.1.2, 78.8.0.?, 312.16.0.?	$[ ]$
62400.o2	62400fe1	62400.o	62400fe	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1.927318139$	$1$	$2$	$124416$	$1.198126$	$7604375/2047032$	$1.24246$	$3.41263$	$[0, -1, 0, 767, 175777]$	$y^2=x^3-x^2+767x+175777$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(21, 448)]$
62400.hu2	62400hu1	62400.hu	62400hu	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{9} \cdot 5^{8} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$	$0$	$622080$	$2.002846$	$7604375/2047032$	$1.24246$	$4.28722$	$[0, 1, 0, 19167, 22010463]$	$y^2=x^3+x^2+19167x+22010463$	3.4.0.a.1, 24.8.0-3.a.1.4, 156.8.0.?, 312.16.0.?	$[ ]$
62400.hx2	62400dc1	62400.hx	62400dc	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{9} \cdot 5^{2} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$0.774044439$	$1$	$4$	$124416$	$1.198126$	$7604375/2047032$	$1.24246$	$3.41263$	$[0, 1, 0, 767, -175777]$	$y^2=x^3+x^2+767x-175777$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[(299, 5184)]$
76050.cu2	76050ct1	76050.cu	76050ct	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3^{15} \cdot 5^{8} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$2.173065745$	$1$	$0$	$4354560$	$2.794903$	$7604375/2047032$	$1.24246$	$5.05744$	$[1, -1, 0, 455508, 2549221416]$	$y^2+xy=x^3-x^2+455508x+2549221416$	3.4.0.a.1, 24.8.0-3.a.1.6, 39.8.0-3.a.1.2, 312.16.0.?	$[(-6171/4, 3092367/4)]$
76050.dn2	76050fa1	76050.dn	76050fa	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3^{15} \cdot 5^{2} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1.310034846$	$1$	$2$	$870912$	$1.990185$	$7604375/2047032$	$1.24246$	$4.19825$	$[1, -1, 1, 18220, 20390127]$	$y^2+xy+y=x^3-x^2+18220x+20390127$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[(23, 4551)]$
95550.bs2	95550cg1	95550.bs	95550cg	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{9} \cdot 5^{8} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$6.590837186$	$1$	$2$	$933120$	$1.936079$	$7604375/2047032$	$1.24246$	$4.05806$	$[1, 1, 0, 14675, 14747125]$	$y^2+xy=x^3+x^2+14675x+14747125$	3.4.0.a.1, 21.8.0-3.a.1.1, 312.8.0.?, 2184.16.0.?	$[(4941, 345013)]$
95550.kd2	95550jp1	95550.kd	95550jp	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{9} \cdot 5^{2} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10920$	$16$	$0$	$0.426629904$	$1$	$4$	$186624$	$1.131359$	$7604375/2047032$	$1.24246$	$3.21597$	$[1, 0, 0, 587, 117977]$	$y^2+xy=x^3+587x+117977$	3.4.0.a.1, 105.8.0.?, 312.8.0.?, 10920.16.0.?	$[(116, 1265)]$
187200.y2	187200io1	187200.y	187200io	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{15} \cdot 5^{8} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1.386445861$	$1$	$4$	$4976640$	$2.552151$	$7604375/2047032$	$1.24246$	$4.44222$	$[0, 0, 0, 172500, 594110000]$	$y^2=x^3+172500x+594110000$	3.4.0.a.1, 24.8.0-3.a.1.1, 78.8.0.?, 312.16.0.?	$[(-650, 14400)]$
187200.bc2	187200co1	187200.bc	187200co	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{15} \cdot 5^{2} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$995328$	$1.747431$	$7604375/2047032$	$1.24246$	$3.64678$	$[0, 0, 0, 6900, -4752880]$	$y^2=x^3+6900x-4752880$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[ ]$
187200.pj2	187200ca1	187200.pj	187200ca	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{15} \cdot 5^{8} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$1$	$1$	$0$	$4976640$	$2.552151$	$7604375/2047032$	$1.24246$	$4.44222$	$[0, 0, 0, 172500, -594110000]$	$y^2=x^3+172500x-594110000$	3.4.0.a.1, 24.8.0-3.a.1.3, 156.8.0.?, 312.16.0.?	$[ ]$
187200.pl2	187200of1	187200.pl	187200of	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{21} \cdot 3^{15} \cdot 5^{2} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$3.604477545$	$1$	$2$	$995328$	$1.747431$	$7604375/2047032$	$1.24246$	$3.64678$	$[0, 0, 0, 6900, 4752880]$	$y^2=x^3+6900x+4752880$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[(2504, 125388)]$
202800.k2	202800df1	202800.k	202800df	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{9} \cdot 5^{8} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$312$	$16$	$0$	$6.719855037$	$1$	$0$	$13063680$	$2.938744$	$7604375/2047032$	$1.24246$	$4.79276$	$[0, -1, 0, 809792, 6042598912]$	$y^2=x^3-x^2+809792x+6042598912$	3.4.0.a.1, 24.8.0-3.a.1.7, 156.8.0.?, 312.16.0.?	$[(-15856/5, 9077328/5)]$
202800.kb2	202800cx1	202800.kb	202800cx	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{9} \cdot 5^{2} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$0.792722279$	$1$	$4$	$2612736$	$2.134026$	$7604375/2047032$	$1.24246$	$4.00253$	$[0, 1, 0, 32392, 48353748]$	$y^2=x^3+x^2+32392x+48353748$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(-308, 3042)]$
235950.f2	235950f1	235950.f	235950f	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{9} \cdot 5^{2} \cdot 11^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$17160$	$16$	$0$	$2.457056144$	$1$	$4$	$933120$	$1.357351$	$7604375/2047032$	$1.24246$	$3.20019$	$[1, 1, 0, 1450, 458220]$	$y^2+xy=x^3+x^2+1450x+458220$	3.4.0.a.1, 165.8.0.?, 312.8.0.?, 17160.16.0.?	$[(-71, 96)]$
235950.iv2	235950iv1	235950.iv	235950iv	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{9} \cdot 5^{8} \cdot 11^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$3432$	$16$	$0$	$0.536518745$	$1$	$4$	$4665600$	$2.162071$	$7604375/2047032$	$1.24246$	$3.98075$	$[1, 0, 0, 36237, 57205017]$	$y^2+xy=x^3+36237x+57205017$	3.4.0.a.1, 33.8.0-3.a.1.2, 312.8.0.?, 3432.16.0.?	$[(252, 8949)]$
286650.ei2	286650ei1	286650.ei	286650ei	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{15} \cdot 5^{2} \cdot 7^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10920$	$16$	$0$	$1$	$1$	$0$	$1492992$	$1.680666$	$7604375/2047032$	$1.24246$	$3.45937$	$[1, -1, 0, 5283, -3185379]$	$y^2+xy=x^3-x^2+5283x-3185379$	3.4.0.a.1, 105.8.0.?, 312.8.0.?, 10920.16.0.?	$[ ]$
286650.mk2	286650mk1	286650.mk	286650mk	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 $	$ - 2^{3} \cdot 3^{15} \cdot 5^{8} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$2184$	$16$	$0$	$3.604021756$	$1$	$2$	$7464960$	$2.485386$	$7604375/2047032$	$1.24246$	$4.22784$	$[1, -1, 1, 132070, -398040303]$	$y^2+xy+y=x^3-x^2+132070x-398040303$	3.4.0.a.1, 21.8.0-3.a.1.2, 312.8.0.?, 2184.16.0.?	$[(10019, 998265)]$

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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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