Elliptic curves over $\Q$ of conductor 5304

Results (28 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
5304.a1	5304i2	5304.a	5304i	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$0.275239678$	$1$		$11$	$2048$	$0.338829$	$238481570896/25857$	$0.93322$	$3.70125$	$[0, -1, 0, -820, 9316]$	\(y^2=x^3-x^2-820x+9316\)	2.3.0.a.1, 34.6.0.a.1, 52.6.0.c.1, 884.12.0.?	$[(4, 78)]$
5304.a2	5304i1	5304.a	5304i	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{4} \cdot 3^{4} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$0.550479356$	$1$		$9$	$1024$	$-0.007744$	$1171019776/304317$	$0.92581$	$2.75806$	$[0, -1, 0, -55, 136]$	\(y^2=x^3-x^2-55x+136\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(1, 9)]$
5304.b1	5304k4	5304.b	5304k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3 \cdot 13 \cdot 17 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$5304$	$48$	$0$	$3.968460214$	$1$		$11$	$6144$	$0.792874$	$305612563186948/663$	$0.94496$	$4.69727$	$[0, -1, 0, -14144, 652188]$	\(y^2=x^3-x^2-14144x+652188\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 52.12.0-4.c.1.2, 104.24.0.?, $\ldots$	$[(78, 132), (73, 58)]$
5304.b2	5304k3	5304.b	5304k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3^{4} \cdot 13 \cdot 17^{4} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$5304$	$48$	$0$	$0.992115053$	$1$		$17$	$6144$	$0.792874$	$161838334948/87947613$	$0.93419$	$3.81769$	$[0, -1, 0, -1144, 4060]$	\(y^2=x^3-x^2-1144x+4060\)	2.3.0.a.1, 4.12.0-4.c.1.2, 26.6.0.b.1, 52.24.0-52.g.1.1, 408.24.0.?, $\ldots$	$[(-18, 136), (33, 34)]$
5304.b3	5304k2	5304.b	5304k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{2} \cdot 13^{2} \cdot 17^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$2652$	$48$	$0$	$0.992115053$	$1$		$33$	$3072$	$0.446301$	$298766385232/439569$	$0.93525$	$3.72753$	$[0, -1, 0, -884, 10404]$	\(y^2=x^3-x^2-884x+10404\)	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.b.1.2, 204.24.0.?, 2652.48.0.?	$[(0, 102), (5, 78)]$
5304.b4	5304k1	5304.b	5304k	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{4} \cdot 3 \cdot 13^{4} \cdot 17 \)	$2$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$5304$	$48$	$0$	$3.968460214$	$1$		$13$	$1536$	$0.099727$	$-420616192/1456611$	$0.95470$	$2.86530$	$[0, -1, 0, -39, 264]$	\(y^2=x^3-x^2-39x+264\)	2.3.0.a.1, 4.12.0-4.c.1.1, 102.6.0.?, 104.24.0.?, 204.24.0.?, $\ldots$	$[(1, 15), (8, 20)]$
5304.c1	5304g1	5304.c	5304g	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3^{4} \cdot 13^{2} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$1$		$1$	$3584$	$0.386240$	$8251733668/232713$	$0.85660$	$3.47066$	$[0, -1, 0, -424, -3140]$	\(y^2=x^3-x^2-424x-3140\)	2.3.0.a.1, 34.6.0.a.1, 104.6.0.?, 1768.12.0.?	$[]$
5304.c2	5304g2	5304.c	5304g	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{11} \cdot 3^{8} \cdot 13 \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1768$	$12$	$0$	$1$	$4$	$2$	$1$	$7168$	$0.732814$	$47279806/24649677$	$0.96128$	$3.74273$	$[0, -1, 0, 96, -10836]$	\(y^2=x^3-x^2+96x-10836\)	2.3.0.a.1, 68.6.0.c.1, 104.6.0.?, 1768.12.0.?	$[]$
5304.d1	5304h2	5304.d	5304h	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3^{4} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$0.981633704$	$1$		$7$	$2048$	$0.373260$	$3822686500/304317$	$0.84928$	$3.38094$	$[0, -1, 0, -328, 2236]$	\(y^2=x^3-x^2-328x+2236\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(22, 72)]$
5304.d2	5304h1	5304.d	5304h	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{2} \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$0.490816852$	$1$		$7$	$1024$	$0.026686$	$137842000/25857$	$0.78659$	$2.83188$	$[0, -1, 0, -68, -156]$	\(y^2=x^3-x^2-68x-156\)	2.3.0.a.1, 34.6.0.a.1, 52.6.0.c.1, 884.12.0.?	$[(-4, 6)]$
5304.e1	5304b2	5304.e	5304b	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3^{8} \cdot 13 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$24576$	$1.767302$	$253674278705546500/2058765672717$	$0.98136$	$5.48101$	$[0, -1, 0, -132928, -18478532]$	\(y^2=x^3-x^2-132928x-18478532\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[]$
5304.e2	5304b1	5304.e	5304b	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{4} \cdot 13^{2} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1$	$1$		$1$	$12288$	$1.420729$	$1008754689437602000/67254057$	$0.98116$	$5.48032$	$[0, -1, 0, -132668, -18555180]$	\(y^2=x^3-x^2-132668x-18555180\)	2.3.0.a.1, 34.6.0.a.1, 52.6.0.c.1, 884.12.0.?	$[]$
5304.f1	5304a1	5304.f	5304a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3^{2} \cdot 13^{4} \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$136$	$12$	$0$	$2.095731629$	$1$		$5$	$7680$	$1.180603$	$315042014258500/1262881737$	$0.94524$	$4.70081$	$[0, -1, 0, -14288, 659868]$	\(y^2=x^3-x^2-14288x+659868\)	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[(74, 48)]$
5304.f2	5304a2	5304.f	5304a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{11} \cdot 3^{4} \cdot 13^{2} \cdot 17^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$136$	$12$	$0$	$4.191463258$	$1$		$3$	$15360$	$1.527176$	$-23040414103250/330419182041$	$0.98369$	$4.85558$	$[0, -1, 0, -7528, 1279084]$	\(y^2=x^3-x^2-7528x+1279084\)	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[(-95, 1062)]$
5304.g1	5304j3	5304.g	5304j	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3^{4} \cdot 13^{4} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$1768$	$48$	$0$	$1$	$1$		$1$	$10240$	$1.174356$	$2753580869496292/39328497$	$0.95806$	$4.95360$	$[0, -1, 0, -29432, -1933668]$	\(y^2=x^3-x^2-29432x-1933668\)	2.3.0.a.1, 4.12.0-4.c.1.2, 34.6.0.a.1, 68.24.0-68.g.1.1, 104.24.0.?, $\ldots$	$[]$
5304.g2	5304j2	5304.g	5304j	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{8} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$884$	$48$	$0$	$1$	$1$		$3$	$5120$	$0.827784$	$2927363579728/320445801$	$0.90371$	$3.99364$	$[0, -1, 0, -1892, -27900]$	\(y^2=x^3-x^2-1892x-27900\)	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.b.1.1, 68.24.0-68.b.1.2, 884.48.0.?	$[]$
5304.g3	5304j1	5304.g	5304j	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{4} \cdot 3^{4} \cdot 13 \cdot 17^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$1768$	$48$	$0$	$1$	$1$		$3$	$2560$	$0.481210$	$618724784128/87947613$	$0.91771$	$3.48913$	$[0, -1, 0, -447, 3312]$	\(y^2=x^3-x^2-447x+3312\)	2.3.0.a.1, 4.12.0-4.c.1.1, 26.6.0.b.1, 52.24.0-52.g.1.2, 136.24.0.?, $\ldots$	$[]$
5304.g4	5304j4	5304.g	5304j	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 13 \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$1768$	$48$	$0$	$1$	$4$	$2$	$1$	$10240$	$1.174356$	$1744147297148/9513325341$	$0.94948$	$4.34341$	$[0, -1, 0, 2528, -142820]$	\(y^2=x^3-x^2+2528x-142820\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 52.12.0-4.c.1.1, 68.12.0-4.c.1.2, $\ldots$	$[]$
5304.h1	5304c2	5304.h	5304c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{2} \cdot 13 \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2652$	$12$	$0$	$0.909532976$	$1$		$5$	$1024$	$0.021933$	$61918288/33813$	$0.82472$	$2.73856$	$[0, -1, 0, -52, 52]$	\(y^2=x^3-x^2-52x+52\)	2.3.0.a.1, 26.6.0.b.1, 204.6.0.?, 2652.12.0.?	$[(-2, 12)]$
5304.h2	5304c1	5304.h	5304c	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{4} \cdot 3 \cdot 13^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2652$	$12$	$0$	$1.819065953$	$1$		$3$	$512$	$-0.324640$	$14047232/8619$	$0.83052$	$2.24231$	$[0, -1, 0, 13, 0]$	\(y^2=x^3-x^2+13x\)	2.3.0.a.1, 52.6.0.c.1, 102.6.0.?, 2652.12.0.?	$[(4, 10)]$
5304.i1	5304l1	5304.i	5304l	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{4} \cdot 3^{6} \cdot 13^{3} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2652$	$12$	$0$	$0.177759476$	$1$		$11$	$2304$	$0.595615$	$1343969093632/462866157$	$0.93614$	$3.57958$	$[0, 1, 0, -579, 3222]$	\(y^2=x^3+x^2-579x+3222\)	2.3.0.a.1, 26.6.0.b.1, 204.6.0.?, 2652.12.0.?	$[(3, 39)]$
5304.i2	5304l2	5304.i	5304l	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{8} \cdot 3^{3} \cdot 13^{6} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2652$	$12$	$0$	$0.355518953$	$1$		$11$	$4608$	$0.942189$	$2181636984368/2215505331$	$0.92209$	$3.95935$	$[0, 1, 0, 1716, 24336]$	\(y^2=x^3+x^2+1716x+24336\)	2.3.0.a.1, 52.6.0.c.1, 102.6.0.?, 2652.12.0.?	$[(0, 156)]$
5304.j1	5304f2	5304.j	5304f	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{2} \cdot 13^{3} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1.082350193$	$1$		$7$	$9216$	$1.107100$	$644811009586000/1651460733$	$0.94094$	$4.62269$	$[0, 1, 0, -11428, 465392]$	\(y^2=x^3+x^2-11428x+465392\)	2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.?	$[(8, 612)]$
5304.j2	5304f1	5304.j	5304f	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( - 2^{4} \cdot 3 \cdot 13^{6} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$2.164700387$	$1$		$3$	$4608$	$0.760526$	$-602275072000/4184843403$	$0.96506$	$3.78512$	$[0, 1, 0, -443, 12810]$	\(y^2=x^3+x^2-443x+12810\)	2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.?	$[(6, 102)]$
5304.k1	5304e2	5304.k	5304e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{2} \cdot 13^{6} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$2.627404647$	$1$		$5$	$4608$	$0.858523$	$1603530178000/738501777$	$0.92097$	$3.92346$	$[0, 1, 0, -1548, 10080]$	\(y^2=x^3+x^2-1548x+10080\)	2.3.0.a.1, 34.6.0.a.1, 52.6.0.c.1, 884.12.0.?	$[(36, 48)]$
5304.k2	5304e1	5304.k	5304e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{4} \cdot 3^{4} \cdot 13^{3} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.313702323$	$1$		$7$	$2304$	$0.511950$	$3322336000000/51429573$	$0.98800$	$3.68511$	$[0, 1, 0, -783, -8586]$	\(y^2=x^3+x^2-783x-8586\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(-15, 3)]$
5304.l1	5304d2	5304.l	5304d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{10} \cdot 3^{16} \cdot 13^{3} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$0.882312365$	$1$		$7$	$36864$	$1.852472$	$64122592551794500/27331783704693$	$0.99192$	$5.32065$	$[0, 1, 0, -84048, 4785840]$	\(y^2=x^3+x^2-84048x+4785840\)	2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.?	$[(12, 1944)]$
5304.l2	5304d1	5304.l	5304d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{8} \cdot 13^{6} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$884$	$12$	$0$	$1.764624731$	$1$		$3$	$18432$	$1.505898$	$27873248949250000/538367795433$	$1.00820$	$5.06186$	$[0, 1, 0, -40108, -3053056]$	\(y^2=x^3+x^2-40108x-3053056\)	2.3.0.a.1, 34.6.0.a.1, 52.6.0.c.1, 884.12.0.?	$[(-112, 216)]$