Elliptic curves over $\Q$ of conductor 36100

Results (17 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
36100.a1	36100j3	36100.a	36100j	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 5^{9} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$2280$	$384$	$9$	$3.612317637$	$1$		$1$	$248832$	$1.896294$	$488095744/125$	$1.07376$	$4.77431$	$[0, 1, 0, -373033, 87550188]$	\(y^2=x^3+x^2-373033x+87550188\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 10.6.0.a.1, $\ldots$	$[(1221/2, 11913/2)]$
36100.a2	36100j4	36100.a	36100j	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( - 2^{8} \cdot 5^{12} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$2280$	$384$	$9$	$7.224635274$	$1$		$1$	$497664$	$2.242867$	$-20720464/15625$	$0.95894$	$4.81695$	$[0, 1, 0, -327908, 109571188]$	\(y^2=x^3+x^2-327908x+109571188\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.24.0.d.1, $\ldots$	$[(18589/6, 1910051/6)]$
36100.a3	36100j1	36100.a	36100j	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 5^{7} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$2280$	$384$	$9$	$1.204105879$	$1$		$7$	$82944$	$1.346989$	$16384/5$	$0.95621$	$3.79262$	$[0, 1, 0, -12033, -353312]$	\(y^2=x^3+x^2-12033x-353312\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 10.6.0.a.1, $\ldots$	$[(-51, 361)]$
36100.a4	36100j2	36100.a	36100j	$4$	$6$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( - 2^{8} \cdot 5^{8} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$2280$	$384$	$9$	$2.408211758$	$1$		$5$	$165888$	$1.693562$	$21296/25$	$0.83964$	$4.08449$	$[0, 1, 0, 33092, -2338812]$	\(y^2=x^3+x^2+33092x-2338812\)	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.24.0.d.1, $\ldots$	$[(188, 3250)]$
36100.b1	36100c2	36100.b	36100c	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 5^{7} \cdot 19^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.017526065$	$1$		$19$	$46080$	$1.078245$	$7888624/5$	$0.82983$	$3.80369$	$[0, 1, 0, -12508, 533988]$	\(y^2=x^3+x^2-12508x+533988\)	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 380.12.0.?	$[(68, 50), (143, 1300)]$
36100.b2	36100c1	36100.b	36100c	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( - 2^{4} \cdot 5^{8} \cdot 19^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.017526065$	$1$		$19$	$23040$	$0.731672$	$-16384/25$	$0.82449$	$3.07390$	$[0, 1, 0, -633, 11488]$	\(y^2=x^3+x^2-633x+11488\)	2.3.0.a.1, 20.6.0.e.1, 38.6.0.b.1, 380.12.0.?	$[(-7, 125), (13, 75)]$
36100.c1	36100d1	36100.c	36100d	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 5^{7} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$689472$	$2.220413$	$1245184/5$	$0.87552$	$5.03067$	$[0, 1, 0, -914533, 335151063]$	\(y^2=x^3+x^2-914533x+335151063\)	10.2.0.a.1	$[]$
36100.d1	36100f1	36100.d	36100f	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 5^{6} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	2.2.0.1, 5.5.0.1	2Cn, 5S4	$380$	$60$	$2$	$2.414377283$	$1$		$2$	$7560$	$0.241865$	$4864$	$0.64811$	$2.55456$	$[0, -1, 0, -158, -563]$	\(y^2=x^3-x^2-158x-563\)	2.2.0.a.1, 5.5.0.a.1, 10.10.0.a.1, 38.6.0.a.1, 190.30.2.?, $\ldots$	$[(-9, 7)]$
36100.e1	36100e2	36100.e	36100e	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 5^{8} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$3.512029690$	$1$		$3$	$414720$	$2.171780$	$472058064/475$	$0.91565$	$5.03534$	$[0, 0, 0, -929575, 344664750]$	\(y^2=x^3-929575x+344664750\)	2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 380.12.0.?	$[(-646, 25992)]$
36100.e2	36100e1	36100.e	36100e	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 5^{7} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$7.024059380$	$1$		$1$	$207360$	$1.825205$	$3538944/1805$	$1.20155$	$4.30484$	$[0, 0, 0, -72200, 2572125]$	\(y^2=x^3-72200x+2572125\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[(98515/9, 30179600/9)]$
36100.f1	36100a1	36100.f	36100a	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 5^{6} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 5$	2.2.0.1, 5.5.0.1	2Cn, 5S4	$380$	$60$	$2$	$1$	$1$		$0$	$143640$	$1.714085$	$4864$	$0.64811$	$4.23805$	$[0, 1, 0, -57158, 4204313]$	\(y^2=x^3+x^2-57158x+4204313\)	2.2.0.a.1, 5.5.0.a.1, 10.10.0.a.1, 20.20.0-10.a.1.1, 38.6.0.a.1, $\ldots$	$[]$
36100.g1	36100g1	36100.g	36100g	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{4} \cdot 5^{11} \cdot 19^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.24	2B	$40$	$48$	$0$	$15.06096148$	$1$		$1$	$2073600$	$2.905312$	$5405726654464/407253125$	$0.99078$	$5.66172$	$[0, -1, 0, -8315033, -8604352438]$	\(y^2=x^3-x^2-8315033x-8604352438\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.4, 10.6.0.a.1, 20.24.0.e.1, $\ldots$	$[(-82954517/239, 275154834999/239)]$
36100.g2	36100g2	36100.g	36100g	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( - 2^{8} \cdot 5^{16} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.38	2B	$40$	$48$	$0$	$30.12192296$	$1$		$1$	$4147200$	$3.251884$	$298091207216/3525390625$	$0.96838$	$5.93253$	$[0, -1, 0, 7975092, -38219799688]$	\(y^2=x^3-x^2+7975092x-38219799688\)	2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.2, 20.12.0.d.1, 40.48.0-40.bc.1.8	$[(521019041957038/162759, 11984759651236548360734/162759)]$
36100.h1	36100b2	36100.h	36100b	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 5^{7} \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$16$	$2$	$1$	$875520$	$2.550465$	$7888624/5$	$0.82983$	$5.48718$	$[0, -1, 0, -4515508, -3689716488]$	\(y^2=x^3-x^2-4515508x-3689716488\)	2.3.0.a.1, 20.6.0.e.1, 76.6.0.?, 380.12.0.?	$[]$
36100.h2	36100b1	36100.h	36100b	$2$	$2$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( - 2^{4} \cdot 5^{8} \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$16$	$2$	$1$	$437760$	$2.203892$	$-16384/25$	$0.82449$	$4.75739$	$[0, -1, 0, -228633, -80167738]$	\(y^2=x^3-x^2-228633x-80167738\)	2.3.0.a.1, 20.6.0.e.1, 38.6.0.b.1, 380.12.0.?	$[]$
36100.i1	36100h1	36100.i	36100h	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( - 2^{8} \cdot 5^{6} \cdot 19^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$5.429362115$	$1$		$0$	$302400$	$1.836008$	$-4194304/19$	$1.07903$	$4.58598$	$[0, -1, 0, -192533, 32707937]$	\(y^2=x^3-x^2-192533x+32707937\)	38.2.0.a.1	$[(15937/8, 193857/8)]$
36100.j1	36100i1	36100.j	36100i	$1$	$1$	\( 2^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 5^{7} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$2.410889399$	$1$		$0$	$36288$	$0.748194$	$1245184/5$	$0.87552$	$3.34718$	$[0, -1, 0, -2533, -48063]$	\(y^2=x^3-x^2-2533x-48063\)	10.2.0.a.1	$[(-257/3, 350/3)]$