Elliptic curves over $\Q$ of conductor 6440

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
6440.a1	6440f2	6440.a	6440f	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 5^{4} \cdot 7^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$1288$	$12$	$0$	$1.815049879$	$1$		$5$	$24576$	$1.445654$	$1357792998752738/38897700625$	$0.92509$	$4.84240$	$[0, 1, 0, -29296, 1871904]$	\(y^2=x^3+x^2-29296x+1871904\)	2.3.0.a.1, 8.6.0.b.1, 644.6.0.?, 1288.12.0.?	$[(19, 1150)]$
6440.a2	6440f1	6440.a	6440f	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{8} \cdot 7^{3} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$1288$	$12$	$0$	$3.630099759$	$1$		$3$	$12288$	$1.099081$	$8564808605476/3081640625$	$0.89688$	$4.18574$	$[0, 1, 0, -4296, -68096]$	\(y^2=x^3+x^2-4296x-68096\)	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[(72, 32)]$
6440.b1	6440h1	6440.b	6440h	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{2} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1.342780211$	$1$		$5$	$1024$	$-0.040798$	$7086244/4025$	$0.89479$	$2.58887$	$[0, 1, 0, -40, 0]$	\(y^2=x^3+x^2-40x\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(8, 16)]$
6440.b2	6440h2	6440.b	6440h	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{11} \cdot 5 \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$2.685560422$	$1$		$3$	$2048$	$0.305776$	$219804478/129605$	$0.84524$	$3.05952$	$[0, 1, 0, 160, 160]$	\(y^2=x^3+x^2+160x+160\)	2.3.0.a.1, 40.6.0.a.1, 644.6.0.?, 6440.12.0.?	$[(3, 26)]$
6440.c1	6440b1	6440.c	6440b	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 23^{3} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$0.098589219$	$1$		$20$	$2688$	$0.482774$	$-5674076449024/14904575$	$1.00612$	$3.66511$	$[0, -1, 0, -936, 11365]$	\(y^2=x^3-x^2-936x+11365\)	46.2.0.a.1	$[(-2, 115), (13, 35)]$
6440.d1	6440a1	6440.d	6440a	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{4} \cdot 5^{4} \cdot 7^{4} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$1.165185889$	$1$		$4$	$3584$	$0.693509$	$-243090490825984/34514375$	$0.90072$	$4.09306$	$[0, -1, 0, -3276, -71099]$	\(y^2=x^3-x^2-3276x-71099\)	46.2.0.a.1	$[(126, 1225)]$
6440.e1	6440d1	6440.e	6440d	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{4} \cdot 5^{6} \cdot 7^{2} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$0.138564404$	$1$		$8$	$1920$	$0.310444$	$28134973184/17609375$	$0.85560$	$3.05952$	$[0, -1, 0, 160, -275]$	\(y^2=x^3-x^2+160x-275\)	46.2.0.a.1	$[(30, 175)]$
6440.f1	6440i1	6440.f	6440i	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 5^{5} \cdot 7^{5} \cdot 23^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$1$	$1$		$0$	$72000$	$2.062500$	$-3840316976122235063296/27784071875$	$1.00070$	$6.29911$	$[0, -1, 0, -2071545, -1146907475]$	\(y^2=x^3-x^2-2071545x-1146907475\)	70.2.0.a.1	$[]$
6440.g1	6440k1	6440.g	6440k	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{4} \cdot 5^{2} \cdot 7^{6} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$46$	$2$	$0$	$0.104075557$	$1$		$8$	$1920$	$0.424336$	$-40535147776/67648175$	$0.84507$	$3.25586$	$[0, -1, 0, -180, 1897]$	\(y^2=x^3-x^2-180x+1897\)	46.2.0.a.1	$[(4, 35)]$
6440.h1	6440e4	6440.h	6440e	$4$	$4$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{4} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6440$	$48$	$0$	$2.009216261$	$1$		$3$	$2560$	$0.651071$	$4407931365156/100625$	$0.89841$	$4.11000$	$[0, 0, 0, -3443, 77758]$	\(y^2=x^3-3443x+77758\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 40.12.0-4.c.1.5, 92.12.0.?, $\ldots$	$[(43, 96)]$
6440.h2	6440e3	6440.h	6440e	$4$	$4$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5 \cdot 7 \cdot 23^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6440$	$48$	$0$	$2.009216261$	$1$		$3$	$2560$	$0.651071$	$84923690436/9794435$	$0.86089$	$3.65969$	$[0, 0, 0, -923, -9658]$	\(y^2=x^3-923x-9658\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 28.12.0-4.c.1.2, 140.24.0.?, $\ldots$	$[(-13, 12)]$
6440.h3	6440e2	6440.h	6440e	$4$	$4$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{8} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3220$	$48$	$0$	$1.004608130$	$1$		$11$	$1280$	$0.304497$	$4790692944/648025$	$0.84837$	$3.17380$	$[0, 0, 0, -223, 1122]$	\(y^2=x^3-223x+1122\)	2.6.0.a.1, 20.12.0-2.a.1.1, 28.12.0-2.a.1.1, 92.12.0.?, 140.24.0.?, $\ldots$	$[(1, 30)]$
6440.h4	6440e1	6440.h	6440e	$4$	$4$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{4} \cdot 5 \cdot 7^{4} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$6440$	$48$	$0$	$2.009216261$	$1$		$3$	$640$	$-0.042077$	$73598976/276115$	$0.87524$	$2.57555$	$[0, 0, 0, 22, 93]$	\(y^2=x^3+22x+93\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 56.12.0-4.c.1.5, 92.12.0.?, $\ldots$	$[(6, 21)]$
6440.i1	6440g1	6440.i	6440g	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{8} \cdot 5^{2} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$0.748936017$	$1$		$7$	$640$	$-0.106505$	$44851536/4025$	$0.75606$	$2.64120$	$[0, 0, 0, -47, 114]$	\(y^2=x^3-47x+114\)	2.3.0.a.1, 20.6.0.b.1, 322.6.0.?, 3220.12.0.?	$[(5, 2)]$
6440.i2	6440g2	6440.i	6440g	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{10} \cdot 5 \cdot 7^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3220$	$12$	$0$	$1.497872035$	$1$		$5$	$1280$	$0.240068$	$16078716/129605$	$0.85853$	$2.97413$	$[0, 0, 0, 53, 534]$	\(y^2=x^3+53x+534\)	2.3.0.a.1, 20.6.0.a.1, 644.6.0.?, 3220.12.0.?	$[(-5, 12)]$
6440.j1	6440c1	6440.j	6440c	$1$	$1$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( - 2^{8} \cdot 5^{3} \cdot 7 \cdot 23^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$70$	$2$	$0$	$0.887716292$	$1$		$4$	$1728$	$0.282203$	$-3525581824/462875$	$0.80077$	$3.16215$	$[0, 1, 0, -201, -1285]$	\(y^2=x^3+x^2-201x-1285\)	70.2.0.a.1	$[(19, 46)]$
6440.k1	6440j2	6440.k	6440j	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{11} \cdot 5^{2} \cdot 7^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$1288$	$12$	$0$	$1$	$1$		$1$	$4608$	$0.575394$	$75933869762/648025$	$0.84656$	$3.72596$	$[0, -1, 0, -1120, 14700]$	\(y^2=x^3-x^2-1120x+14700\)	2.3.0.a.1, 8.6.0.b.1, 644.6.0.?, 1288.12.0.?	$[]$
6440.k2	6440j1	6440.k	6440j	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{4} \cdot 7 \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$1288$	$12$	$0$	$1$	$1$		$1$	$2304$	$0.228820$	$188183524/100625$	$0.93120$	$2.96278$	$[0, -1, 0, -120, -100]$	\(y^2=x^3-x^2-120x-100\)	2.3.0.a.1, 8.6.0.c.1, 322.6.0.?, 1288.12.0.?	$[]$