Elliptic curves over $\Q$ of conductor 4026

Results (18 matches)

 

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
4026.a1	4026a1	4026.a	4026a	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{7} \cdot 3^{3} \cdot 11 \cdot 61 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$16104$	$2$	$0$	$1$	$1$		$0$	$672$	$-0.008020$	$-62146192681/2318976$	$0.85789$	$3.00165$	$[1, 1, 0, -82, -332]$	\(y^2+xy=x^3+x^2-82x-332\)	16104.2.0.?	$[]$
4026.b1	4026c2	4026.b	4026c	$2$	$3$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{9} \cdot 3^{7} \cdot 11^{6} \cdot 61^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$1464$	$16$	$0$	$0.608785879$	$1$		$4$	$81648$	$2.066319$	$-105416929096482457/450261029485960704$	$1.05913$	$5.79523$	$[1, 0, 1, -9842, -32287228]$	\(y^2+xy+y=x^3-9842x-32287228\)	3.8.0-3.a.1.1, 1464.16.0.?	$[(2460, 120556)]$
4026.b2	4026c1	4026.b	4026c	$2$	$3$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{3} \cdot 3^{21} \cdot 11^{2} \cdot 61 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$1464$	$16$	$0$	$1.826357639$	$1$		$4$	$27216$	$1.517012$	$144595657865303/617662935930744$	$1.03975$	$5.00107$	$[1, 0, 1, 1093, 1195742]$	\(y^2+xy+y=x^3+1093x+1195742\)	3.8.0-3.a.1.2, 1464.16.0.?	$[(270, 4468)]$
4026.c1	4026d1	4026.c	4026d	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{7} \cdot 3 \cdot 11^{2} \cdot 61 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1464$	$2$	$0$	$1$	$1$		$0$	$1456$	$-0.024226$	$-25750777177/2834304$	$0.85128$	$2.90895$	$[1, 0, 1, -62, -208]$	\(y^2+xy+y=x^3-62x-208\)	1464.2.0.?	$[]$
4026.d1	4026e2	4026.d	4026e	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( 2 \cdot 3^{2} \cdot 11 \cdot 61^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$16104$	$12$	$0$	$1$	$1$		$0$	$1184$	$-0.023059$	$161789533849/736758$	$0.86596$	$3.10939$	$[1, 0, 1, -114, 454]$	\(y^2+xy+y=x^3-114x+454\)	2.3.0.a.1, 88.6.0.?, 732.6.0.?, 16104.12.0.?	$[]$
4026.d2	4026e1	4026.d	4026e	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{2} \cdot 3 \cdot 11^{2} \cdot 61 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$16104$	$12$	$0$	$1$	$1$		$1$	$592$	$-0.369632$	$-4826809/88572$	$0.92973$	$2.27423$	$[1, 0, 1, -4, 14]$	\(y^2+xy+y=x^3-4x+14\)	2.3.0.a.1, 88.6.0.?, 366.6.0.?, 16104.12.0.?	$[]$
4026.e1	4026b2	4026.e	4026b	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( 2^{5} \cdot 3^{18} \cdot 11^{3} \cdot 61^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$16104$	$12$	$0$	$1$	$1$		$0$	$116640$	$1.970280$	$913488720932053621369/61400271112522848$	$0.99598$	$5.81455$	$[1, 0, 1, -202144, 32870414]$	\(y^2+xy+y=x^3-202144x+32870414\)	2.3.0.a.1, 88.6.0.?, 732.6.0.?, 16104.12.0.?	$[]$
4026.e2	4026b1	4026.e	4026b	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{10} \cdot 3^{9} \cdot 11^{6} \cdot 61 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$16104$	$12$	$0$	$1$	$1$		$1$	$58320$	$1.623707$	$139952759660884871/2178096890821632$	$0.99870$	$5.14835$	$[1, 0, 1, 10816, 2204174]$	\(y^2+xy+y=x^3+10816x+2204174\)	2.3.0.a.1, 88.6.0.?, 366.6.0.?, 16104.12.0.?	$[]$
4026.f1	4026f1	4026.f	4026f	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{7} \cdot 3 \cdot 11^{7} \cdot 61^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$16104$	$2$	$0$	$1$	$1$		$0$	$23520$	$1.601759$	$14704504384534271/1698515543328384$	$1.01322$	$5.12235$	$[1, 1, 1, 5104, 1980017]$	\(y^2+xy+y=x^3+x^2+5104x+1980017\)	16104.2.0.?	$[]$
4026.g1	4026h2	4026.g	4026h	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( 2^{2} \cdot 3^{3} \cdot 11^{2} \cdot 61^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8052$	$12$	$0$	$1$	$1$		$0$	$2496$	$0.352724$	$19632741836833/48626028$	$0.90543$	$3.68750$	$[1, 1, 1, -562, 4883]$	\(y^2+xy+y=x^3+x^2-562x+4883\)	2.3.0.a.1, 12.6.0.a.1, 2684.6.0.?, 8052.12.0.?	$[]$
4026.g2	4026h1	4026.g	4026h	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{4} \cdot 3^{6} \cdot 11 \cdot 61 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8052$	$12$	$0$	$1$	$1$		$1$	$1248$	$0.006151$	$-1180932193/7826544$	$0.86807$	$2.82048$	$[1, 1, 1, -22, 131]$	\(y^2+xy+y=x^3+x^2-22x+131\)	2.3.0.a.1, 12.6.0.b.1, 1342.6.0.?, 8052.12.0.?	$[]$
4026.h1	4026g1	4026.h	4026g	$1$	$1$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{17} \cdot 3^{19} \cdot 11 \cdot 61 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$16104$	$2$	$0$	$1$	$1$		$0$	$51680$	$1.953007$	$167084491388439286943/102220096386760704$	$1.02073$	$5.60989$	$[1, 1, 1, 114746, 3624899]$	\(y^2+xy+y=x^3+x^2+114746x+3624899\)	16104.2.0.?	$[]$
4026.i1	4026i4	4026.i	4026i	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( 2^{3} \cdot 3^{2} \cdot 11^{3} \cdot 61^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$16104$	$96$	$1$	$1$	$1$		$0$	$31968$	$1.700819$	$8551551109433208625/4937300515763352$	$1.04800$	$5.25179$	$[1, 0, 0, -42603, 159705]$	\(y^2+xy=x^3-42603x+159705\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 88.6.0.?, 264.48.0.?, $\ldots$	$[]$
4026.i2	4026i2	4026.i	4026i	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( 2^{9} \cdot 3^{6} \cdot 11 \cdot 61^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$16104$	$96$	$1$	$1$	$1$		$4$	$10656$	$1.151514$	$2986886106831048625/15277413888$	$0.97233$	$5.12507$	$[1, 0, 0, -30003, 1997793]$	\(y^2+xy=x^3-30003x+1997793\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 88.6.0.?, 264.48.0.?, $\ldots$	$[]$
4026.i3	4026i1	4026.i	4026i	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{18} \cdot 3^{3} \cdot 11^{2} \cdot 61 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$16104$	$96$	$1$	$1$	$1$		$5$	$5328$	$0.804939$	$-692332063944625/52241891328$	$0.93094$	$4.13150$	$[1, 0, 0, -1843, 32225]$	\(y^2+xy=x^3-1843x+32225\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 88.6.0.?, 264.48.0.?, $\ldots$	$[]$
4026.i4	4026i3	4026.i	4026i	$4$	$6$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{6} \cdot 3 \cdot 11^{6} \cdot 61^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$16104$	$96$	$1$	$1$	$1$		$1$	$15984$	$1.354246$	$133100178546359375/77205251969472$	$1.07977$	$4.75029$	$[1, 0, 0, 10637, 21281]$	\(y^2+xy=x^3+10637x+21281\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 88.6.0.?, 264.48.0.?, $\ldots$	$[]$
4026.j1	4026j2	4026.j	4026j	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 61^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8052$	$12$	$0$	$1$	$1$		$0$	$1408$	$0.213149$	$1567768622113/21611568$	$0.94411$	$3.38300$	$[1, 0, 0, -242, -1452]$	\(y^2+xy=x^3-242x-1452\)	2.3.0.a.1, 12.6.0.a.1, 2684.6.0.?, 8052.12.0.?	$[]$
4026.j2	4026j1	4026.j	4026j	$2$	$2$	\( 2 \cdot 3 \cdot 11 \cdot 61 \)	\( - 2^{8} \cdot 3^{2} \cdot 11 \cdot 61 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8052$	$12$	$0$	$1$	$1$		$1$	$704$	$-0.133425$	$-912673/1545984$	$0.99650$	$2.61504$	$[1, 0, 0, -2, -60]$	\(y^2+xy=x^3-2x-60\)	2.3.0.a.1, 12.6.0.b.1, 1342.6.0.?, 8052.12.0.?	$[]$