Elliptic curve search results

Results (33 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	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
664.b1	664c1	664.b	664c	$1$	$1$	\( 2^{3} \cdot 83 \)	\( - 2^{4} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.207011953$	$1$		$6$	$16$	$-0.688087$	$-256000/83$	$0.71692$	$2.41146$	$[0, -1, 0, -3, 4]$	\(y^2=x^3-x^2-3x+4\)	166.2.0.?	$[(1, 1)]$
1328.d1	1328a1	1328.d	1328a	$1$	$1$	\( 2^{4} \cdot 83 \)	\( - 2^{4} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.693364324$	$1$		$2$	$32$	$-0.688087$	$-256000/83$	$0.71692$	$2.17903$	$[0, 1, 0, -3, -4]$	\(y^2=x^3+x^2-3x-4\)	166.2.0.?	$[(4, 8)]$
5312.e1	5312o1	5312.e	5312o	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{10} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.236223482$	$1$		$2$	$256$	$-0.341513$	$-256000/83$	$0.71692$	$2.31171$	$[0, -1, 0, -13, -19]$	\(y^2=x^3-x^2-13x-19\)	166.2.0.?	$[(5, 4)]$
5312.j1	5312a1	5312.j	5312a	$1$	$1$	\( 2^{6} \cdot 83 \)	\( - 2^{10} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.718975858$	$1$		$2$	$256$	$-0.341513$	$-256000/83$	$0.71692$	$2.31171$	$[0, 1, 0, -13, 19]$	\(y^2=x^3+x^2-13x+19\)	166.2.0.?	$[(3, 4)]$
5976.b1	5976b1	5976.b	5976b	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$480$	$-0.138780$	$-256000/83$	$0.71692$	$2.56018$	$[0, 0, 0, -30, -79]$	\(y^2=x^3-30x-79\)	166.2.0.?	$[ ]$
11952.g1	11952d1	11952.g	11952d	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.602477074$	$1$		$2$	$960$	$-0.138780$	$-256000/83$	$0.71692$	$2.37116$	$[0, 0, 0, -30, 79]$	\(y^2=x^3-30x+79\)	166.2.0.?	$[(3, 4)]$
16600.i1	16600b1	16600.i	16600b	$1$	$1$	\( 2^{3} \cdot 5^{2} \cdot 83 \)	\( - 2^{4} \cdot 5^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.697310133$	$1$		$4$	$2304$	$0.116633$	$-256000/83$	$0.71692$	$2.60642$	$[0, 1, 0, -83, 338]$	\(y^2=x^3+x^2-83x+338\)	166.2.0.?	$[(-7, 25)]$
32536.f1	32536d1	32536.f	32536d	$1$	$1$	\( 2^{3} \cdot 7^{2} \cdot 83 \)	\( - 2^{4} \cdot 7^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$5.009553215$	$1$		$0$	$6048$	$0.284869$	$-256000/83$	$0.71692$	$2.63191$	$[0, 1, 0, -163, -1058]$	\(y^2=x^3+x^2-163x-1058\)	166.2.0.?	$[(139/3, 503/3)]$
33200.p1	33200h1	33200.p	33200h	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 83 \)	\( - 2^{4} \cdot 5^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$4608$	$0.116633$	$-256000/83$	$0.71692$	$2.43288$	$[0, -1, 0, -83, -338]$	\(y^2=x^3-x^2-83x-338\)	166.2.0.?	$[ ]$
47808.bj1	47808bl1	47808.bj	47808bl	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 83 \)	\( - 2^{10} \cdot 3^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.745532534$	$1$		$2$	$7680$	$0.207793$	$-256000/83$	$0.71692$	$2.45207$	$[0, 0, 0, -120, 632]$	\(y^2=x^3-120x+632\)	166.2.0.?	$[(2, 20)]$
47808.bk1	47808t1	47808.bk	47808t	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 83 \)	\( - 2^{10} \cdot 3^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$4.488252711$	$1$		$0$	$7680$	$0.207793$	$-256000/83$	$0.71692$	$2.45207$	$[0, 0, 0, -120, -632]$	\(y^2=x^3-120x-632\)	166.2.0.?	$[(118/3, 188/3)]$
55112.b1	55112c1	55112.b	55112c	$1$	$1$	\( 2^{3} \cdot 83^{2} \)	\( - 2^{4} \cdot 83^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$110208$	$1.521334$	$-256000/83$	$0.71692$	$3.86397$	$[0, -1, 0, -22963, -1665352]$	\(y^2=x^3-x^2-22963x-1665352\)	166.2.0.?	$[ ]$
65072.h1	65072e1	65072.h	65072e	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 83 \)	\( - 2^{4} \cdot 7^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$3.113588334$	$1$		$2$	$12096$	$0.284869$	$-256000/83$	$0.71692$	$2.46731$	$[0, -1, 0, -163, 1058]$	\(y^2=x^3-x^2-163x+1058\)	166.2.0.?	$[(-14, 20)]$
80344.b1	80344c1	80344.b	80344c	$1$	$1$	\( 2^{3} \cdot 11^{2} \cdot 83 \)	\( - 2^{4} \cdot 11^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$22880$	$0.510861$	$-256000/83$	$0.71692$	$2.66137$	$[0, -1, 0, -403, -3760]$	\(y^2=x^3-x^2-403x-3760\)	166.2.0.?	$[ ]$
110224.g1	110224c1	110224.g	110224c	$1$	$1$	\( 2^{4} \cdot 83^{2} \)	\( - 2^{4} \cdot 83^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$220416$	$1.521334$	$-256000/83$	$0.71692$	$3.63328$	$[0, 1, 0, -22963, 1665352]$	\(y^2=x^3+x^2-22963x+1665352\)	166.2.0.?	$[ ]$
112216.b1	112216b1	112216.b	112216b	$1$	$1$	\( 2^{3} \cdot 13^{2} \cdot 83 \)	\( - 2^{4} \cdot 13^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$0.768530821$	$1$		$4$	$34560$	$0.594388$	$-256000/83$	$0.71692$	$2.67110$	$[0, -1, 0, -563, 6616]$	\(y^2=x^3-x^2-563x+6616\)	166.2.0.?	$[(35, 169)]$
132800.u1	132800cp1	132800.u	132800cp	$1$	$1$	\( 2^{6} \cdot 5^{2} \cdot 83 \)	\( - 2^{10} \cdot 5^{6} \cdot 83 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.686455897$	$1$		$10$	$36864$	$0.463206$	$-256000/83$	$0.71692$	$2.49952$	$[0, -1, 0, -333, 3037]$	\(y^2=x^3-x^2-333x+3037\)	166.2.0.?	$[(12, 25), (37, 200)]$
132800.db1	132800bp1	132800.db	132800bp	$1$	$1$	\( 2^{6} \cdot 5^{2} \cdot 83 \)	\( - 2^{10} \cdot 5^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$36864$	$0.463206$	$-256000/83$	$0.71692$	$2.49952$	$[0, 1, 0, -333, -3037]$	\(y^2=x^3+x^2-333x-3037\)	166.2.0.?	$[ ]$
149400.s1	149400q1	149400.s	149400q	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$69120$	$0.665938$	$-256000/83$	$0.71692$	$2.67900$	$[0, 0, 0, -750, -9875]$	\(y^2=x^3-750x-9875\)	166.2.0.?	$[ ]$
160688.n1	160688o1	160688.n	160688o	$1$	$1$	\( 2^{4} \cdot 11^{2} \cdot 83 \)	\( - 2^{4} \cdot 11^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$7.445517764$	$1$		$0$	$45760$	$0.510861$	$-256000/83$	$0.71692$	$2.50748$	$[0, 1, 0, -403, 3760]$	\(y^2=x^3+x^2-403x+3760\)	166.2.0.?	$[(1488/7, 49048/7)]$
191896.f1	191896d1	191896.f	191896d	$1$	$1$	\( 2^{3} \cdot 17^{2} \cdot 83 \)	\( - 2^{4} \cdot 17^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$3.299968323$	$1$		$2$	$80640$	$0.728520$	$-256000/83$	$0.71692$	$2.68561$	$[0, 1, 0, -963, 14054]$	\(y^2=x^3+x^2-963x+14054\)	166.2.0.?	$[(-5, 137)]$
224432.l1	224432r1	224432.l	224432r	$1$	$1$	\( 2^{4} \cdot 13^{2} \cdot 83 \)	\( - 2^{4} \cdot 13^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$69120$	$0.594388$	$-256000/83$	$0.71692$	$2.52084$	$[0, 1, 0, -563, -6616]$	\(y^2=x^3+x^2-563x-6616\)	166.2.0.?	$[ ]$
239704.g1	239704g1	239704.g	239704g	$1$	$1$	\( 2^{3} \cdot 19^{2} \cdot 83 \)	\( - 2^{4} \cdot 19^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$5.796368862$	$1$		$0$	$110592$	$0.784133$	$-256000/83$	$0.71692$	$2.69125$	$[0, 1, 0, -1203, -20470]$	\(y^2=x^3+x^2-1203x-20470\)	166.2.0.?	$[(7117/9, 545471/9)]$
260288.u1	260288u1	260288.u	260288u	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 83 \)	\( - 2^{10} \cdot 7^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$6.620070661$	$1$		$0$	$96768$	$0.631442$	$-256000/83$	$0.71692$	$2.52653$	$[0, -1, 0, -653, -7811]$	\(y^2=x^3-x^2-653x-7811\)	166.2.0.?	$[(1121/5, 28244/5)]$
260288.bw1	260288bw1	260288.bw	260288bw	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 83 \)	\( - 2^{10} \cdot 7^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$2.700043776$	$1$		$2$	$96768$	$0.631442$	$-256000/83$	$0.71692$	$2.52653$	$[0, 1, 0, -653, 7811]$	\(y^2=x^3+x^2-653x+7811\)	166.2.0.?	$[(-1, 92)]$
292824.y1	292824y1	292824.y	292824y	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$181440$	$0.834175$	$-256000/83$	$0.71692$	$2.69616$	$[0, 0, 0, -1470, 27097]$	\(y^2=x^3-1470x+27097\)	166.2.0.?	$[ ]$
298800.eh1	298800eh1	298800.eh	298800eh	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 83 \)	\( - 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$138240$	$0.665938$	$-256000/83$	$0.71692$	$2.53171$	$[0, 0, 0, -750, 9875]$	\(y^2=x^3-750x+9875\)	166.2.0.?	$[ ]$
351256.d1	351256d1	351256.d	351256d	$1$	$1$	\( 2^{3} \cdot 23^{2} \cdot 83 \)	\( - 2^{4} \cdot 23^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.143995544$	$1$		$4$	$202752$	$0.879661$	$-256000/83$	$0.71692$	$2.70049$	$[0, -1, 0, -1763, -35012]$	\(y^2=x^3-x^2-1763x-35012\)	166.2.0.?	$[(77, 529)]$
383792.h1	383792h1	383792.h	383792h	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 83 \)	\( - 2^{4} \cdot 17^{6} \cdot 83 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$8.905218758$	$1$		$0$	$161280$	$0.728520$	$-256000/83$	$0.71692$	$2.54083$	$[0, -1, 0, -963, -14054]$	\(y^2=x^3-x^2-963x-14054\)	166.2.0.?	$[(5130/11, 185996/11)]$
440896.j1	440896j1	440896.j	440896j	$1$	$1$	\( 2^{6} \cdot 83^{2} \)	\( - 2^{10} \cdot 83^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1.807205524$	$1$		$2$	$1763328$	$1.867908$	$-256000/83$	$0.71692$	$3.56573$	$[0, -1, 0, -91853, 13414669]$	\(y^2=x^3-x^2-91853x+13414669\)	166.2.0.?	$[(941, 27556)]$
440896.bb1	440896bb1	440896.bb	440896bb	$1$	$1$	\( 2^{6} \cdot 83^{2} \)	\( - 2^{10} \cdot 83^{7} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$17.77358271$	$1$		$2$	$1763328$	$1.867908$	$-256000/83$	$0.71692$	$3.56573$	$[0, 1, 0, -91853, -13414669]$	\(y^2=x^3+x^2-91853x-13414669\)	166.2.0.?	$[(470, 6889), (14155636195/4971, 1358349514980004/4971)]$
479408.o1	479408o1	479408.o	479408o	$1$	$1$	\( 2^{4} \cdot 19^{2} \cdot 83 \)	\( - 2^{4} \cdot 19^{6} \cdot 83 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$221184$	$0.784133$	$-256000/83$	$0.71692$	$2.54864$	$[0, -1, 0, -1203, 20470]$	\(y^2=x^3-x^2-1203x+20470\)	166.2.0.?	$[ ]$
496008.i1	496008i1	496008.i	496008i	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 83^{2} \)	\( - 2^{4} \cdot 3^{6} \cdot 83^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$166$	$2$	$0$	$1$	$1$		$0$	$3306240$	$2.070641$	$-256000/83$	$0.71692$	$3.71922$	$[0, 0, 0, -206670, 45171173]$	\(y^2=x^3-206670x+45171173\)	166.2.0.?	$[ ]$

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