Elliptic curves over $\Q$ of conductor 6422

Results (16 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
6422.a1	6422a1	6422.a	6422a	$1$	$1$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{13} \cdot 13^{9} \cdot 19^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$1$	$1$		$0$	$52416$	$1.921377$	$-110931033861649/6497214464$	$0.94569$	$5.45493$	$[1, 1, 0, -169172, 28034128]$	\(y^2+xy=x^3+x^2-169172x+28034128\)	104.2.0.?	$[]$
6422.b1	6422b2	6422.b	6422b	$2$	$5$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2 \cdot 13^{6} \cdot 19^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$9880$	$48$	$1$	$1$	$1$		$0$	$23400$	$1.300259$	$-37966934881/4952198$	$0.97714$	$4.55694$	$[1, 1, 0, -11833, -553405]$	\(y^2+xy=x^3+x^2-11833x-553405\)	5.12.0.a.2, 65.24.0-5.a.2.1, 152.2.0.?, 760.24.1.?, 9880.48.1.?	$[]$
6422.b2	6422b1	6422.b	6422b	$2$	$5$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{5} \cdot 13^{6} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$9880$	$48$	$1$	$1$	$1$		$0$	$4680$	$0.495540$	$-1/608$	$1.37833$	$3.33671$	$[1, 1, 0, -3, 2605]$	\(y^2+xy=x^3+x^2-3x+2605\)	5.12.0.a.1, 65.24.0-5.a.1.1, 152.2.0.?, 760.24.1.?, 9880.48.1.?	$[]$
6422.c1	6422d1	6422.c	6422d	$1$	$1$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{35} \cdot 13^{9} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$21.75813916$	$1$		$0$	$567840$	$3.116100$	$-251347109804029/12403865550848$	$1.04840$	$6.92330$	$[1, 0, 1, -2888552, -17551703882]$	\(y^2+xy+y=x^3-2888552x-17551703882\)	104.2.0.?	$[(118203532399/2810, 40103595044205737/2810)]$
6422.d1	6422c1	6422.d	6422c	$1$	$1$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{4} \cdot 13^{8} \cdot 19^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$152$	$4$	$0$	$1$	$1$		$0$	$22464$	$1.180307$	$-77086633/5776$	$0.84480$	$4.42565$	$[1, 1, 0, -8284, -311904]$	\(y^2+xy=x^3+x^2-8284x-311904\)	4.2.0.a.1, 152.4.0.?	$[]$
6422.e1	6422i1	6422.e	6422i	$1$	$1$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{5} \cdot 13^{7} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$0.207636531$	$1$		$8$	$6720$	$0.964297$	$214921799/150176$	$0.86097$	$3.94360$	$[1, 1, 1, 2109, 17857]$	\(y^2+xy+y=x^3+x^2+2109x+17857\)	104.2.0.?	$[(5, 166)]$
6422.f1	6422e4	6422.f	6422e	$4$	$4$	\( 2 \cdot 13^{2} \cdot 19 \)	\( 2 \cdot 13^{10} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1976$	$48$	$0$	$1$	$1$		$0$	$22848$	$1.354704$	$969417177273/1085318$	$0.93818$	$4.90331$	$[1, -1, 1, -34846, 2509927]$	\(y^2+xy+y=x^3-x^2-34846x+2509927\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 104.24.0.?, 152.24.0.?, $\ldots$	$[]$
6422.f2	6422e3	6422.f	6422e	$4$	$4$	\( 2 \cdot 13^{2} \cdot 19 \)	\( 2 \cdot 13^{7} \cdot 19^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1976$	$48$	$0$	$1$	$1$		$0$	$22848$	$1.354704$	$345505073913/3388346$	$0.97212$	$4.78563$	$[1, -1, 1, -24706, -1475769]$	\(y^2+xy+y=x^3-x^2-24706x-1475769\)	2.3.0.a.1, 4.12.0-4.c.1.2, 104.24.0.?, 152.24.0.?, 1976.48.0.?	$[]$
6422.f3	6422e2	6422.f	6422e	$4$	$4$	\( 2 \cdot 13^{2} \cdot 19 \)	\( 2^{2} \cdot 13^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1976$	$48$	$0$	$1$	$1$		$2$	$11424$	$1.008131$	$469097433/244036$	$0.96358$	$4.03263$	$[1, -1, 1, -2736, 18191]$	\(y^2+xy+y=x^3-x^2-2736x+18191\)	2.6.0.a.1, 4.12.0-2.a.1.1, 104.24.0.?, 152.24.0.?, 988.24.0.?, $\ldots$	$[]$
6422.f4	6422e1	6422.f	6422e	$4$	$4$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{4} \cdot 13^{7} \cdot 19 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1976$	$48$	$0$	$1$	$1$		$3$	$5712$	$0.661557$	$6128487/3952$	$0.83799$	$3.53786$	$[1, -1, 1, 644, 1967]$	\(y^2+xy+y=x^3-x^2+644x+1967\)	2.3.0.a.1, 4.12.0-4.c.1.1, 104.24.0.?, 152.24.0.?, 494.6.0.?, $\ldots$	$[]$
6422.g1	6422j1	6422.g	6422j	$1$	$1$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{35} \cdot 13^{3} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$0.260274423$	$1$		$8$	$43680$	$1.833628$	$-251347109804029/12403865550848$	$1.04840$	$5.16799$	$[1, 0, 0, -17092, -7990256]$	\(y^2+xy=x^3-17092x-7990256\)	104.2.0.?	$[(264, 2300)]$
6422.h1	6422f3	6422.h	6422f	$3$	$9$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{27} \cdot 13^{6} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$53352$	$1296$	$43$	$1$	$1$		$0$	$36936$	$1.767645$	$-69173457625/2550136832$	$1.05462$	$5.07779$	$[1, 0, 0, -14453, -5380831]$	\(y^2+xy=x^3-14453x-5380831\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 39.8.0-3.a.1.2, 117.24.0.?, $\ldots$	$[]$
6422.h2	6422f1	6422.h	6422f	$3$	$9$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{3} \cdot 13^{6} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$53352$	$1296$	$43$	$1$	$1$		$0$	$4104$	$0.669032$	$-413493625/152$	$0.93281$	$4.01831$	$[1, 0, 0, -2623, 51505]$	\(y^2+xy=x^3-2623x+51505\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 39.8.0-3.a.1.1, 117.24.0.?, $\ldots$	$[]$
6422.h3	6422f2	6422.h	6422f	$3$	$9$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{9} \cdot 13^{6} \cdot 19^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$53352$	$1296$	$43$	$1$	$1$		$0$	$12312$	$1.218338$	$94196375/3511808$	$1.01875$	$4.32284$	$[1, 0, 0, 1602, 196676]$	\(y^2+xy=x^3+1602x+196676\)	3.12.0.a.1, 9.36.0.b.1, 39.24.0-3.a.1.1, 117.72.0.?, 152.2.0.?, $\ldots$	$[]$
6422.i1	6422g1	6422.i	6422g	$1$	$1$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2^{4} \cdot 13^{2} \cdot 19^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	4.2.0.1		$1976$	$4$	$0$	$1$	$1$		$0$	$1728$	$-0.102168$	$-77086633/5776$	$0.84480$	$2.67033$	$[1, 1, 1, -49, -161]$	\(y^2+xy+y=x^3+x^2-49x-161\)	4.2.0.a.1, 1976.4.0.?	$[]$
6422.j1	6422h1	6422.j	6422h	$1$	$1$	\( 2 \cdot 13^{2} \cdot 19 \)	\( - 2 \cdot 13^{7} \cdot 19^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$1$	$4$	$2$	$0$	$25536$	$1.012236$	$-25334470953/9386$	$0.90338$	$4.48769$	$[1, -1, 1, -10341, -402281]$	\(y^2+xy+y=x^3-x^2-10341x-402281\)	104.2.0.?	$[]$