Elliptic curve search results

Results (15 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	Manin constant
4641.b2	4641b3	4641.b	4641b	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.6	2Cs	$37128$	$192$	$1$	$1.043339852$	$1$		$8$	$6144$	$1.035313$	$3275619238041697/1605271262049$	$0.94091$	$4.23151$	$[1, 1, 1, -3094, -27214]$	\(y^2+xy+y=x^3+x^2-3094x-27214\)	2.6.0.a.1, 4.24.0-4.b.1.1, 68.48.0-68.c.1.2, 104.48.0.?, 168.48.0.?, $\ldots$	$[(-22, 186)]$	$1$
13923.i2	13923f3	13923.i	13923f	$6$	$8$	\( 3^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{10} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$37128$	$192$	$1$	$3.736513305$	$1$		$4$	$49152$	$1.584620$	$3275619238041697/1605271262049$	$0.94091$	$4.43514$	$[1, -1, 0, -27846, 706927]$	\(y^2+xy=x^3-x^2-27846x+706927\)	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.1, 56.24.0-4.b.1.2, 68.24.0.c.1, $\ldots$	$[(2522, 125099)]$	$1$
32487.e2	32487m4	32487.e	32487m	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 7^{10} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$37128$	$192$	$1$	$4.128525294$	$1$		$6$	$294912$	$2.008266$	$3275619238041697/1605271262049$	$0.94091$	$4.56277$	$[1, 0, 0, -151607, 8879520]$	\(y^2+xy=x^3-151607x+8879520\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.2, 28.24.0-4.b.1.1, 68.24.0.c.1, $\ldots$	$[(-365, 4135)]$	$1$
60333.l2	60333d4	60333.l	60333d	$6$	$8$	\( 3 \cdot 7 \cdot 13^{2} \cdot 17 \)	\( 3^{4} \cdot 7^{4} \cdot 13^{10} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.11	2Cs	$37128$	$192$	$1$	$11.39526251$	$1$		$2$	$1032192$	$2.317787$	$3275619238041697/1605271262049$	$0.94091$	$4.64359$	$[1, 1, 0, -522889, -57174320]$	\(y^2+xy=x^3+x^2-522889x-57174320\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.8, 52.24.0-4.b.1.1, 68.24.0.c.1, $\ldots$	$[(-135145/22, 88746065/22)]$	$1$
74256.cd2	74256dd4	74256.cd	74256dd	$6$	$8$	\( 2^{4} \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.5	2Cs	$37128$	$192$	$1$	$1$	$1$		$7$	$393216$	$1.728460$	$3275619238041697/1605271262049$	$0.94091$	$3.92706$	$[0, 1, 0, -49504, 1642676]$	\(y^2=x^3+x^2-49504x+1642676\)	2.6.0.a.1, 4.24.0-4.b.1.3, 68.48.0-68.c.1.1, 104.48.0.?, 168.48.0.?, $\ldots$	$[ ]$	$1$
78897.g2	78897l4	78897.g	78897l	$6$	$8$	\( 3 \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.3	2Cs	$37128$	$192$	$1$	$1$	$1$		$2$	$1769472$	$2.451920$	$3275619238041697/1605271262049$	$0.94091$	$4.67586$	$[1, 0, 0, -894172, -127442305]$	\(y^2+xy=x^3-894172x-127442305\)	2.6.0.a.1, 4.24.0-4.b.1.2, 68.48.0-68.c.1.3, 104.48.0.?, 168.48.0.?, $\ldots$	$[ ]$	$1$
97461.s2	97461l4	97461.s	97461l	$6$	$8$	\( 3^{2} \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{10} \cdot 7^{10} \cdot 13^{4} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.17	2Cs	$37128$	$192$	$1$	$1$	$4$	$2$	$2$	$2359296$	$2.557575$	$3275619238041697/1605271262049$	$0.94091$	$4.70022$	$[1, -1, 0, -1364463, -239747040]$	\(y^2+xy=x^3-x^2-1364463x-239747040\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 68.24.0.c.1, 84.24.0.?, $\ldots$	$[ ]$	$1$
116025.bq2	116025bg4	116025.bq	116025bg	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5^{6} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$185640$	$192$	$1$	$1.800236105$	$1$		$8$	$786432$	$1.840033$	$3275619238041697/1605271262049$	$0.94091$	$3.89158$	$[1, 0, 1, -77351, -3247027]$	\(y^2+xy+y=x^3-77351x-3247027\)	2.6.0.a.1, 4.12.0.b.1, 20.24.0-4.b.1.1, 68.24.0.c.1, 104.24.0.?, $\ldots$	$[(633, 13879)]$	$1$
180999.f2	180999e3	180999.f	180999e	$6$	$8$	\( 3^{2} \cdot 7 \cdot 13^{2} \cdot 17 \)	\( 3^{10} \cdot 7^{4} \cdot 13^{10} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$37128$	$192$	$1$	$3.223607780$	$1$		$8$	$8257536$	$2.867092$	$3275619238041697/1605271262049$	$0.94091$	$4.76668$	$[1, -1, 1, -4706006, 1539000636]$	\(y^2+xy+y=x^3-x^2-4706006x+1539000636\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.7, 56.24.0-4.b.1.5, 68.24.0.c.1, $\ldots$	$[(182, 26148)]$	$1$
222768.fc2	222768bu4	222768.fc	222768bu	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{10} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$37128$	$192$	$1$	$1.413991050$	$1$		$11$	$3145728$	$2.277767$	$3275619238041697/1605271262049$	$0.94091$	$4.11200$	$[0, 0, 0, -445539, -44797790]$	\(y^2=x^3-445539x-44797790\)	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.3, 56.24.0-4.b.1.7, 68.24.0.c.1, $\ldots$	$[(-337, 8190)]$	$1$
236691.r2	236691r3	236691.r	236691r	$6$	$8$	\( 3^{2} \cdot 7 \cdot 13 \cdot 17^{2} \)	\( 3^{10} \cdot 7^{4} \cdot 13^{4} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$37128$	$192$	$1$	$1$	$1$		$2$	$14155776$	$3.001225$	$3275619238041697/1605271262049$	$0.94091$	$4.79342$	$[1, -1, 0, -8047548, 3440942235]$	\(y^2+xy=x^3-x^2-8047548x+3440942235\)	2.6.0.a.1, 4.12.0.b.1, 12.24.0-4.b.1.2, 56.24.0-4.b.1.2, 68.24.0.c.1, $\ldots$	$[ ]$	$1$
297024.dd2	297024dd3	297024.dd	297024dd	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.21	2Cs	$37128$	$192$	$1$	$1$	$1$		$3$	$3145728$	$2.075035$	$3275619238041697/1605271262049$	$0.94091$	$3.82507$	$[0, -1, 0, -198017, 13339425]$	\(y^2=x^3-x^2-198017x+13339425\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.2, 68.24.0.c.1, 104.48.0.?, $\ldots$	$[ ]$	$1$
297024.gv2	297024gv4	297024.gv	297024gv	$6$	$8$	\( 2^{6} \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{4} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.20	2Cs	$37128$	$192$	$1$	$6.843244955$	$1$		$5$	$3145728$	$2.075035$	$3275619238041697/1605271262049$	$0.94091$	$3.82507$	$[0, 1, 0, -198017, -13339425]$	\(y^2=x^3+x^2-198017x-13339425\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.11, 68.24.0.c.1, 104.48.0.?, $\ldots$	$[(97275, 30338880)]$	$1$
348075.z2	348075z3	348075.z	348075z	$6$	$8$	\( 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \cdot 17 \)	\( 3^{10} \cdot 5^{6} \cdot 7^{4} \cdot 13^{4} \cdot 17^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$185640$	$192$	$1$	$3.558634080$	$1$		$24$	$6291456$	$2.389339$	$3275619238041697/1605271262049$	$0.94091$	$4.07311$	$[1, -1, 1, -696155, 87669722]$	\(y^2+xy+y=x^3-x^2-696155x+87669722\)	2.6.0.a.1, 4.12.0.b.1, 60.24.0-4.b.1.1, 68.24.0.c.1, 104.24.0.?, $\ldots$	$[(54, 7060), (1650, 57733)]$	$1$
422331.br2	422331br3	422331.br	422331br	$6$	$8$	\( 3 \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{4} \cdot 7^{10} \cdot 13^{10} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$37128$	$192$	$1$	$16.83461041$	$1$		$2$	$49545216$	$3.290741$	$3275619238041697/1605271262049$	$0.94091$	$4.84736$	$[1, 0, 1, -25621587, 19533927025]$	\(y^2+xy+y=x^3-25621587x+19533927025\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0-4.b.1.5, 56.24.0-4.b.1.7, 68.24.0.c.1, $\ldots$	$[(-105763339/163, 1055651884203/163)]$	$1$

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