Elliptic curves over $\Q$ of conductor 5160

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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
5160.a1	5160b1	5160.a	5160b	$1$	$1$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 43 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$86$	$2$	$0$	$0.097342123$	$1$		$30$	$1024$	$-0.060075$	$-30505984/9675$	$0.77867$	$2.71569$	$[0, -1, 0, -41, 141]$	\(y^2=x^3-x^2-41x+141\)	86.2.0.?	$[(1, 10), (5, 6)]$
5160.b1	5160g2	5160.b	5160g	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{11} \cdot 3^{10} \cdot 5 \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$6400$	$1.027973$	$2727138195938/545908005$	$0.92415$	$4.24146$	$[0, -1, 0, -3696, -68724]$	\(y^2=x^3-x^2-3696x-68724\)	2.3.0.a.1, 40.6.0.b.1, 516.6.0.?, 5160.12.0.?	$[ ]$
5160.b2	5160g1	5160.b	5160g	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{10} \cdot 3^{5} \cdot 5^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$3200$	$0.681400$	$4615962240676/261225$	$0.91641$	$4.22193$	$[0, -1, 0, -3496, -78404]$	\(y^2=x^3-x^2-3496x-78404\)	2.3.0.a.1, 40.6.0.c.1, 258.6.0.?, 5160.12.0.?	$[ ]$
5160.c1	5160i2	5160.c	5160i	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{11} \cdot 3^{2} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5160$	$12$	$0$	$2.357319856$	$1$		$3$	$1792$	$0.318580$	$909513218/83205$	$0.84154$	$3.30495$	$[0, -1, 0, -256, -1364]$	\(y^2=x^3-x^2-256x-1364\)	2.3.0.a.1, 40.6.0.b.1, 516.6.0.?, 5160.12.0.?	$[(-7, 6)]$
5160.c2	5160i1	5160.c	5160i	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{10} \cdot 3 \cdot 5^{2} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1.178659928$	$1$		$5$	$896$	$-0.027994$	$19307236/3225$	$0.89206$	$2.77323$	$[0, -1, 0, -56, 156]$	\(y^2=x^3-x^2-56x+156\)	2.3.0.a.1, 40.6.0.c.1, 258.6.0.?, 5160.12.0.?	$[(1, 10)]$
5160.d1	5160j1	5160.d	5160j	$1$	$1$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{8} \cdot 3^{44} \cdot 5^{4} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$86$	$2$	$0$	$13.07034368$	$1$		$0$	$3153920$	$4.027351$	$27554726454844416496885738496/26465717996184551883676875$	$1.08222$	$8.30901$	$[0, -1, 0, 399549679, 2496643493445]$	\(y^2=x^3-x^2+399549679x+2496643493445\)	86.2.0.?	$[(770528077163/2489, 685476882728132850/2489)]$
5160.e1	5160h1	5160.e	5160h	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{8} \cdot 3 \cdot 5^{2} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$0.729796929$	$1$		$7$	$768$	$-0.141499$	$20720464/3225$	$0.75125$	$2.61933$	$[0, -1, 0, -36, -60]$	\(y^2=x^3-x^2-36x-60\)	2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.?	$[(-4, 2)]$
5160.e2	5160h2	5160.e	5160h	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{10} \cdot 3^{2} \cdot 5 \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2580$	$12$	$0$	$1.459593859$	$1$		$5$	$1536$	$0.205075$	$27871484/83205$	$0.82823$	$2.98289$	$[0, -1, 0, 64, -420]$	\(y^2=x^3-x^2+64x-420\)	2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.?	$[(6, 12)]$
5160.f1	5160a1	5160.f	5160a	$1$	$1$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{11} \cdot 3^{8} \cdot 5 \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$3.710423560$	$1$		$2$	$2816$	$0.608199$	$-71157653138/1410615$	$0.88710$	$3.81888$	$[0, -1, 0, -1096, -13844]$	\(y^2=x^3-x^2-1096x-13844\)	1720.2.0.?	$[(349, 6480)]$
5160.g1	5160k1	5160.g	5160k	$1$	$1$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{11} \cdot 3^{4} \cdot 5^{11} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1720$	$2$	$0$	$4.255569348$	$1$		$2$	$21120$	$1.470755$	$9002230481662/170068359375$	$0.98348$	$4.78526$	$[0, -1, 0, 5504, 882220]$	\(y^2=x^3-x^2+5504x+882220\)	1720.2.0.?	$[(121, 1818)]$
5160.h1	5160c1	5160.h	5160c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{4} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$1032$	$12$	$0$	$1.527557675$	$1$		$5$	$2304$	$0.417706$	$3550014724/725625$	$0.99630$	$3.38317$	$[0, -1, 0, -320, -1668]$	\(y^2=x^3-x^2-320x-1668\)	2.3.0.a.1, 8.6.0.d.1, 258.6.0.?, 1032.12.0.?	$[(-11, 20)]$
5160.h2	5160c2	5160.h	5160c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{11} \cdot 3^{6} \cdot 5^{2} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$1032$	$12$	$0$	$3.055115350$	$1$		$3$	$4608$	$0.764279$	$16954370638/33698025$	$0.90384$	$3.75124$	$[0, -1, 0, 680, -10868]$	\(y^2=x^3-x^2+680x-10868\)	2.3.0.a.1, 8.6.0.a.1, 516.6.0.?, 1032.12.0.?	$[(29, 180)]$
5160.i1	5160e3	5160.i	5160e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{11} \cdot 3^{4} \cdot 5 \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5160$	$48$	$0$	$1$	$1$		$1$	$6144$	$0.793679$	$41725476313778/17415$	$0.93732$	$4.56055$	$[0, 1, 0, -9176, 335280]$	\(y^2=x^3+x^2-9176x+335280\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0-4.c.1.2, 120.24.0.?, $\ldots$	$[ ]$
5160.i2	5160e2	5160.i	5160e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 43^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$5160$	$48$	$0$	$1$	$1$		$3$	$3072$	$0.447105$	$20674973956/416025$	$0.86747$	$3.58928$	$[0, 1, 0, -576, 5040]$	\(y^2=x^3+x^2-576x+5040\)	2.6.0.a.1, 12.12.0-2.a.1.1, 40.12.0-2.a.1.1, 120.24.0.?, 172.12.0.?, $\ldots$	$[ ]$
5160.i3	5160e1	5160.i	5160e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{8} \cdot 3 \cdot 5^{4} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5160$	$48$	$0$	$1$	$1$		$1$	$1536$	$0.100532$	$192143824/80625$	$0.81096$	$2.87985$	$[0, 1, 0, -76, -160]$	\(y^2=x^3+x^2-76x-160\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.4, 120.24.0.?, $\ldots$	$[ ]$
5160.i4	5160e4	5160.i	5160e	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{11} \cdot 3 \cdot 5 \cdot 43^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$5160$	$48$	$0$	$1$	$4$	$2$	$1$	$6144$	$0.793679$	$715822/51282015$	$1.03514$	$3.84061$	$[0, 1, 0, 24, 15600]$	\(y^2=x^3+x^2+24x+15600\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0-4.c.1.1, 120.24.0.?, $\ldots$	$[ ]$
5160.j1	5160f1	5160.j	5160f	$1$	$1$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{8} \cdot 3^{4} \cdot 5^{4} \cdot 43^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$86$	$2$	$0$	$0.111310849$	$1$		$12$	$6144$	$0.985730$	$-162140591104/4025041875$	$0.97179$	$4.11042$	$[0, 1, 0, -721, -49645]$	\(y^2=x^3+x^2-721x-49645\)	86.2.0.?	$[(347, 6450)]$
5160.k1	5160l2	5160.k	5160l	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{11} \cdot 3^{5} \cdot 5^{6} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$9600$	$1.240017$	$34064240990978/7020421875$	$1.00268$	$4.53682$	$[0, 1, 0, -8576, -248160]$	\(y^2=x^3+x^2-8576x-248160\)	2.3.0.a.1, 24.6.0.a.1, 860.6.0.?, 5160.12.0.?	$[ ]$
5160.k2	5160l1	5160.k	5160l	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{10} \cdot 3^{10} \cdot 5^{3} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5160$	$12$	$0$	$1$	$1$		$1$	$4800$	$0.893443$	$161555647964/317388375$	$0.98613$	$3.93193$	$[0, 1, 0, 1144, -22656]$	\(y^2=x^3+x^2+1144x-22656\)	2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.?	$[ ]$
5160.l1	5160d3	5160.l	5160d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{11} \cdot 3^{5} \cdot 5^{2} \cdot 43^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$1032$	$48$	$0$	$1$	$1$		$1$	$40960$	$1.730839$	$947094050118111698/20769216075$	$0.99077$	$5.73384$	$[0, 1, 0, -259816, 50886320]$	\(y^2=x^3+x^2-259816x+50886320\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.1, 24.24.0-24.s.1.4, $\ldots$	$[ ]$
5160.l2	5160d2	5160.l	5160d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{10} \cdot 3^{10} \cdot 5^{4} \cdot 43^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1032$	$48$	$0$	$1$	$1$		$3$	$20480$	$1.384264$	$513591322675396/68238500625$	$0.95257$	$4.77312$	$[0, 1, 0, -16816, 731120]$	\(y^2=x^3+x^2-16816x+731120\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.b.1.2, 172.12.0.?, $\ldots$	$[ ]$
5160.l3	5160d1	5160.l	5160d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{8} \cdot 3^{5} \cdot 5^{8} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$1032$	$48$	$0$	$1$	$1$		$1$	$10240$	$1.037691$	$34739908901584/4081640625$	$0.92466$	$4.29587$	$[0, 1, 0, -4316, -98880]$	\(y^2=x^3+x^2-4316x-98880\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 24.24.0-24.y.1.2, $\ldots$	$[ ]$
5160.l4	5160d4	5160.l	5160d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{11} \cdot 3^{20} \cdot 5^{2} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$1032$	$48$	$0$	$1$	$1$		$1$	$40960$	$1.730839$	$969360123836302/3748293231075$	$0.98630$	$5.13173$	$[0, 1, 0, 26184, 3895920]$	\(y^2=x^3+x^2+26184x+3895920\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 24.24.0-24.y.1.8, 172.12.0.?, $\ldots$	$[ ]$
5160.m1	5160n3	5160.m	5160n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{10} \cdot 3 \cdot 5^{12} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$5160$	$48$	$0$	$1.441918754$	$1$		$3$	$9216$	$1.281534$	$54477543627364/31494140625$	$1.04568$	$4.51066$	$[0, 1, 0, -7960, -11392]$	\(y^2=x^3+x^2-7960x-11392\)	2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.ba.1.12, 258.6.0.?, 516.24.0.?, $\ldots$	$[(136, 1200)]$
5160.m2	5160n2	5160.m	5160n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{8} \cdot 3^{2} \cdot 5^{6} \cdot 43^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2580$	$48$	$0$	$0.720959377$	$1$		$13$	$4608$	$0.934961$	$67283921459536/260015625$	$1.00288$	$4.37320$	$[0, 1, 0, -5380, 149600]$	\(y^2=x^3+x^2-5380x+149600\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.a.1.1, 516.24.0.?, 2580.48.0.?	$[(50, 90)]$
5160.m3	5160n1	5160.m	5160n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{4} \cdot 3 \cdot 5^{3} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$5160$	$48$	$0$	$1.441918754$	$1$		$3$	$2304$	$0.588387$	$1073544204384256/16125$	$0.97030$	$4.37287$	$[0, 1, 0, -5375, 149898]$	\(y^2=x^3+x^2-5375x+149898\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 40.24.0-40.ba.1.10, $\ldots$	$[(51, 105)]$
5160.m4	5160n4	5160.m	5160n	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{10} \cdot 3^{4} \cdot 5^{3} \cdot 43^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$5160$	$48$	$0$	$1.441918754$	$1$		$7$	$9216$	$1.281534$	$-2580786074884/34615360125$	$1.04688$	$4.52654$	$[0, 1, 0, -2880, 291600]$	\(y^2=x^3+x^2-2880x+291600\)	2.3.0.a.1, 4.12.0-4.c.1.1, 20.24.0-20.h.1.2, 1032.24.0.?, 5160.48.0.?	$[(0, 540)]$
5160.n1	5160m4	5160.n	5160m	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{11} \cdot 3^{3} \cdot 5 \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$5160$	$48$	$0$	$1$	$4$	$2$	$1$	$16896$	$1.411953$	$820480625548035842/5805$	$0.99016$	$5.71705$	$[0, 1, 0, -247680, 47361888]$	\(y^2=x^3+x^2-247680x+47361888\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 24.24.0-24.y.1.6, 860.12.0.?, $\ldots$	$[ ]$
5160.n2	5160m3	5160.n	5160m	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{11} \cdot 3^{3} \cdot 5^{4} \cdot 43^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$5160$	$48$	$0$	$1$	$1$		$1$	$16896$	$1.411953$	$245245463376482/57692266875$	$0.95595$	$4.76774$	$[0, 1, 0, -16560, 626400]$	\(y^2=x^3+x^2-16560x+626400\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.s.1.1, 1720.24.0.?, 5160.48.0.?	$[ ]$
5160.n3	5160m2	5160.n	5160m	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( 2^{10} \cdot 3^{6} \cdot 5^{2} \cdot 43^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$5160$	$48$	$0$	$1$	$1$		$3$	$8448$	$1.065378$	$400649568576484/33698025$	$0.94741$	$4.74407$	$[0, 1, 0, -15480, 736128]$	\(y^2=x^3+x^2-15480x+736128\)	2.6.0.a.1, 4.12.0-2.a.1.1, 24.24.0-24.b.1.4, 860.24.0.?, 5160.48.0.?	$[ ]$
5160.n4	5160m1	5160.n	5160m	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \cdot 43 \)	\( - 2^{8} \cdot 3^{12} \cdot 5 \cdot 43 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$5160$	$48$	$0$	$1$	$1$		$3$	$4224$	$0.718805$	$-315278049616/114259815$	$0.89070$	$3.80271$	$[0, 1, 0, -900, 12960]$	\(y^2=x^3+x^2-900x+12960\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.y.1.4, 430.6.0.?, 860.24.0.?, $\ldots$	$[ ]$

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