Elliptic curve search results

Results (26 matches)

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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
2730.x5	2730x1	2730.x	2730x	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.48.0.32	2B	$4368$	$192$	$1$	$0.975453197$	$1$		$11$	$6144$	$0.963550$	$-5602762882081/801531494400$	$0.99253$	$4.40701$	$[1, 1, 1, -370, 43007]$	\(y^2+xy+y=x^3+x^2-370x+43007\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.e.2.7, 56.48.0-56.bv.1.2, $\ldots$	$[(-3, 211)]$
8190.i5	8190n1	8190.i	8190n	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{24} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$49152$	$1.512856$	$-5602762882081/801531494400$	$0.99253$	$4.60124$	$[1, -1, 0, -3330, -1164524]$	\(y^2+xy=x^3-x^2-3330x-1164524\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.e.2, $\ldots$	$[ ]$
13650.x5	13650z1	13650.x	13650z	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{24} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$1$	$1$		$1$	$147456$	$1.768269$	$-5602762882081/801531494400$	$0.99253$	$4.67628$	$[1, 0, 1, -9251, 5394398]$	\(y^2+xy+y=x^3-9251x+5394398\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 20.12.0-4.c.1.2, $\ldots$	$[ ]$
19110.cn5	19110cp1	19110.cn	19110cp	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.94	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$294912$	$1.936504$	$-5602762882081/801531494400$	$0.99253$	$4.72146$	$[1, 0, 0, -18131, -14805855]$	\(y^2+xy=x^3-18131x-14805855\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.e.2.2, 28.12.0-4.c.1.2, $\ldots$	$[ ]$
21840.cc5	21840cg1	21840.cc	21840cg	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{36} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.48	2B	$4368$	$192$	$1$	$8.960867652$	$1$		$1$	$147456$	$1.656696$	$-5602762882081/801531494400$	$0.99253$	$4.32231$	$[0, 1, 0, -5920, -2764300]$	\(y^2=x^3+x^2-5920x-2764300\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 56.48.0-56.bv.1.10, $\ldots$	$[(10945/8, 573375/8)]$
35490.d5	35490a1	35490.d	35490a	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1.735636817$	$1$		$7$	$1032192$	$2.246025$	$-5602762882081/801531494400$	$0.99253$	$4.79700$	$[1, 1, 0, -62533, 94799437]$	\(y^2+xy=x^3+x^2-62533x+94799437\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.e.2, $\ldots$	$[(-489, 3202)]$
40950.dy5	40950ds1	40950.dy	40950ds	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{24} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$0.884316536$	$1$		$9$	$1179648$	$2.317574$	$-5602762882081/801531494400$	$0.99253$	$4.81321$	$[1, -1, 1, -83255, -145648753]$	\(y^2+xy+y=x^3-x^2-83255x-145648753\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 56.24.0.bv.1, $\ldots$	$[(739, 13630)]$
57330.cr5	57330ci1	57330.cr	57330ci	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{24} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$1$	$2359296$	$2.485809$	$-5602762882081/801531494400$	$0.99253$	$4.84966$	$[1, -1, 0, -163179, 399758085]$	\(y^2+xy=x^3-x^2-163179x+399758085\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.8, $\ldots$	$[ ]$
65520.e5	65520cv1	65520.e	65520cv	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{36} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$1179648$	$2.206005$	$-5602762882081/801531494400$	$0.99253$	$4.48850$	$[0, 0, 0, -53283, 74582818]$	\(y^2=x^3-53283x+74582818\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0.e.2, $\ldots$	$[ ]$
87360.b5	87360ec1	87360.b	87360ec	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{42} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.185	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$1179648$	$2.003269$	$-5602762882081/801531494400$	$0.99253$	$4.16119$	$[0, -1, 0, -23681, -22090719]$	\(y^2=x^3-x^2-23681x-22090719\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 16.48.0-16.e.2.8, 56.48.0-56.bv.1.1, $\ldots$	$[ ]$
87360.ff5	87360ck1	87360.ff	87360ck	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{42} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.194	2B	$4368$	$192$	$1$	$8.027497763$	$1$		$1$	$1179648$	$2.003269$	$-5602762882081/801531494400$	$0.99253$	$4.16119$	$[0, 1, 0, -23681, 22090719]$	\(y^2=x^3+x^2-23681x+22090719\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 16.48.0-16.e.2.6, 56.48.0-56.bv.1.9, $\ldots$	$[(7413/2, 637329/2)]$
95550.m5	95550bt1	95550.m	95550bt	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{24} \cdot 3 \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$12.38300773$	$1$		$1$	$7077888$	$2.741222$	$-5602762882081/801531494400$	$0.99253$	$4.90090$	$[1, 1, 0, -453275, -1850731875]$	\(y^2+xy=x^3+x^2-453275x-1850731875\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 40.24.0-8.n.1.8, $\ldots$	$[(723175/23, 105030600/23)]$
106470.ex5	106470fi1	106470.ex	106470fi	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{24} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 13^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.38	2B	$4368$	$192$	$1$	$1$	$1$		$3$	$8257536$	$2.795330$	$-5602762882081/801531494400$	$0.99253$	$4.91118$	$[1, -1, 1, -562802, -2560147599]$	\(y^2+xy+y=x^3-x^2-562802x-2560147599\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 16.48.0-16.e.2.10, 56.48.0-56.bv.1.15, $\ldots$	$[ ]$
109200.dm5	109200ds1	109200.dm	109200ds	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{36} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$9.502497535$	$1$		$1$	$3538944$	$2.461414$	$-5602762882081/801531494400$	$0.99253$	$4.55506$	$[0, -1, 0, -148008, -345241488]$	\(y^2=x^3-x^2-148008x-345241488\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 20.12.0-4.c.1.1, $\ldots$	$[(138157/9, 48144250/9)]$
152880.ci5	152880ez1	152880.ci	152880ez	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{36} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.166	2B	$4368$	$192$	$1$	$11.07433129$	$1$		$1$	$7077888$	$2.629654$	$-5602762882081/801531494400$	$0.99253$	$4.59579$	$[0, -1, 0, -290096, 947574720]$	\(y^2=x^3-x^2-290096x+947574720\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 16.48.0-16.e.2.4, 28.12.0-4.c.1.1, $\ldots$	$[(93649/17, 146362216/17)]$
177450.kh5	177450bi1	177450.kh	177450bi	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \)	\( - 2^{24} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$1$	$1$		$1$	$24772608$	$3.050743$	$-5602762882081/801531494400$	$0.99253$	$4.95720$	$[1, 0, 0, -1563338, 11853056292]$	\(y^2+xy=x^3-1563338x+11853056292\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 56.24.0.bv.1, $\ldots$	$[ ]$
248430.fd5	248430fd1	248430.fd	248430fd	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{8} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1$	$16$	$2$	$1$	$49545216$	$3.218979$	$-5602762882081/801531494400$	$0.99253$	$4.98544$	$[1, 0, 1, -3064143, -32525399294]$	\(y^2+xy+y=x^3-3064143x-32525399294\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.8, $\ldots$	$[ ]$
262080.kc5	262080kc1	262080.kc	262080kc	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{42} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$9437184$	$2.552578$	$-5602762882081/801531494400$	$0.99253$	$4.32311$	$[0, 0, 0, -213132, 596662544]$	\(y^2=x^3-213132x+596662544\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.11, $\ldots$	$[ ]$
262080.ku5	262080ku1	262080.ku	262080ku	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{42} \cdot 3^{7} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1$	$4$	$2$	$1$	$9437184$	$2.552578$	$-5602762882081/801531494400$	$0.99253$	$4.32311$	$[0, 0, 0, -213132, -596662544]$	\(y^2=x^3-213132x-596662544\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.9, $\ldots$	$[ ]$
283920.fl5	283920fl1	283920.fl	283920fl	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \)	\( - 2^{36} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$1$	$1$		$1$	$24772608$	$2.939171$	$-5602762882081/801531494400$	$0.99253$	$4.66501$	$[0, 1, 0, -1000536, -6069165036]$	\(y^2=x^3+x^2-1000536x-6069165036\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0.e.2, $\ldots$	$[ ]$
286650.qs5	286650qs1	286650.qs	286650qs	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2^{24} \cdot 3^{7} \cdot 5^{8} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$1.142830608$	$1$		$9$	$56623104$	$3.290531$	$-5602762882081/801531494400$	$0.99253$	$4.99699$	$[1, -1, 1, -4079480, 49965681147]$	\(y^2+xy+y=x^3-x^2-4079480x+49965681147\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 56.24.0.bv.1, $\ldots$	$[(3629, 286185)]$
327600.hm5	327600hm1	327600.hm	327600hm	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{36} \cdot 3^{7} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$1$	$1$		$1$	$28311552$	$3.010723$	$-5602762882081/801531494400$	$0.99253$	$4.68006$	$[0, 0, 0, -1332075, 9322852250]$	\(y^2=x^3-1332075x+9322852250\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 56.24.0.bv.1, $\ldots$	$[ ]$
330330.bc5	330330bc1	330330.bc	330330bc	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 13 \)	\( - 2^{24} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{6} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$48048$	$192$	$1$	$5.592599198$	$1$		$3$	$7864320$	$2.162498$	$-5602762882081/801531494400$	$0.99253$	$3.87602$	$[1, 1, 0, -44772, -57466416]$	\(y^2+xy=x^3+x^2-44772x-57466416\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 44.12.0-4.c.1.2, $\ldots$	$[(6353, 502906)]$
436800.fb5	436800fb1	436800.fb	436800fb	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{42} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$1$	$28311552$	$2.807991$	$-5602762882081/801531494400$	$0.99253$	$4.38907$	$[0, -1, 0, -592033, 2762523937]$	\(y^2=x^3-x^2-592033x+2762523937\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 40.24.0-8.n.1.6, $\ldots$	$[ ]$
436800.qi5	436800qi1	436800.qi	436800qi	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	\( - 2^{42} \cdot 3 \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$21840$	$192$	$1$	$20.25759995$	$1$		$1$	$28311552$	$2.807991$	$-5602762882081/801531494400$	$0.99253$	$4.38907$	$[0, 1, 0, -592033, -2762523937]$	\(y^2=x^3+x^2-592033x-2762523937\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 40.24.0-8.n.1.2, $\ldots$	$[(2725603153/664, 140360620469625/664)]$
458640.ib5	458640ib1	458640.ib	458640ib	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)	\( - 2^{36} \cdot 3^{7} \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$4368$	$192$	$1$	$7.517916651$	$1$		$3$	$56623104$	$3.178959$	$-5602762882081/801531494400$	$0.99253$	$4.71413$	$[0, 0, 0, -2610867, -25581906574]$	\(y^2=x^3-2610867x-25581906574\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 24.24.0-8.n.1.4, $\ldots$	$[(1051817, 1078722560)]$

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