Elliptic curve search results

Results (18 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
3315.a2	3315b2	3315.a	3315b	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$1.356343459$	$1$		$26$	$896$	$0.058381$	$39616946929/10989225$	$0.84706$	$3.01035$	$[1, 1, 1, -71, -196]$	\(y^2+xy+y=x^3+x^2-71x-196\)	2.6.0.a.1, 12.12.0-2.a.1.1, 68.12.0-2.a.1.1, 204.24.0.?, 260.12.0.?, $\ldots$	$[(-4, 8), (22, 86)]$	$1$
9945.h2	9945k2	9945.h	9945k	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$13260$	$48$	$0$	$2.067717358$	$1$		$6$	$7168$	$0.607688$	$39616946929/10989225$	$0.84706$	$3.36717$	$[1, -1, 0, -639, 4648]$	\(y^2+xy=x^3-x^2-639x+4648\)	2.6.0.a.1, 4.12.0-2.a.1.1, 204.24.0.?, 780.24.0.?, 4420.24.0.?, $\ldots$	$[(24, 40)]$	$1$
16575.j2	16575h2	16575.j	16575h	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{8} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$5.053177091$	$1$		$2$	$21504$	$0.863100$	$39616946929/10989225$	$0.84706$	$3.50560$	$[1, 0, 1, -1776, -20927]$	\(y^2+xy+y=x^3-1776x-20927\)	2.6.0.a.1, 52.12.0-2.a.1.1, 60.12.0-2.a.1.1, 204.12.0.?, 340.12.0.?, $\ldots$	$[(-101/2, 811/2)]$	$1$
43095.n2	43095f2	43095.n	43095f	$4$	$4$	\( 3 \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 13^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$1$	$4$	$2$	$2$	$150528$	$1.340857$	$39616946929/10989225$	$0.84706$	$3.72895$	$[1, 1, 0, -12002, -370209]$	\(y^2+xy=x^3+x^2-12002x-370209\)	2.6.0.a.1, 20.12.0-2.a.1.1, 156.12.0.?, 204.12.0.?, 780.24.0.?, $\ldots$	$[ ]$	$1$
49725.k2	49725f2	49725.k	49725f	$4$	$4$	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 5^{8} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$1$	$1$		$2$	$172032$	$1.412407$	$39616946929/10989225$	$0.84706$	$3.75900$	$[1, -1, 1, -15980, 565022]$	\(y^2+xy+y=x^3-x^2-15980x+565022\)	2.6.0.a.1, 20.12.0-2.a.1.1, 156.12.0.?, 204.12.0.?, 780.24.0.?, $\ldots$	$[ ]$	$1$
53040.ce2	53040co2	53040.ce	53040co	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$1$	$1$		$3$	$57344$	$0.751529$	$39616946929/10989225$	$0.84706$	$3.00771$	$[0, 1, 0, -1136, 10260]$	\(y^2=x^3+x^2-1136x+10260\)	2.6.0.a.1, 12.12.0-2.a.1.1, 68.12.0-2.a.1.1, 204.24.0.?, 260.12.0.?, $\ldots$	$[ ]$	$1$
56355.n2	56355x2	56355.n	56355x	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$13260$	$48$	$0$	$1$	$4$	$2$	$2$	$258048$	$1.474989$	$39616946929/10989225$	$0.84706$	$3.78464$	$[1, 0, 0, -20525, -818400]$	\(y^2+xy=x^3-20525x-818400\)	2.6.0.a.1, 4.12.0-2.a.1.1, 204.24.0.?, 780.24.0.?, 4420.24.0.?, $\ldots$	$[ ]$	$1$
129285.f2	129285w2	129285.f	129285w	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13^{2} \cdot 17 \)	\( 3^{8} \cdot 5^{2} \cdot 13^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$3.227225233$	$1$		$8$	$1204224$	$1.890162$	$39616946929/10989225$	$0.84706$	$3.94093$	$[1, -1, 1, -108023, 9887622]$	\(y^2+xy+y=x^3-x^2-108023x+9887622\)	2.6.0.a.1, 52.12.0-2.a.1.1, 60.12.0-2.a.1.1, 204.12.0.?, 340.12.0.?, $\ldots$	$[(270, 456)]$	$1$
159120.ej2	159120w2	159120.ej	159120w	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{8} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$13260$	$48$	$0$	$1$	$1$		$3$	$458752$	$1.300835$	$39616946929/10989225$	$0.84706$	$3.28217$	$[0, 0, 0, -10227, -287246]$	\(y^2=x^3-10227x-287246\)	2.6.0.a.1, 4.12.0-2.a.1.1, 204.24.0.?, 780.24.0.?, 4420.24.0.?, $\ldots$	$[ ]$	$1$
162435.ba2	162435l2	162435.ba	162435l	$4$	$4$	\( 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$92820$	$48$	$0$	$1.625972933$	$1$		$8$	$258048$	$1.031336$	$39616946929/10989225$	$0.84706$	$3.00699$	$[1, 0, 0, -3480, 56727]$	\(y^2+xy=x^3-3480x+56727\)	2.6.0.a.1, 84.12.0.?, 204.12.0.?, 476.12.0.?, 780.12.0.?, $\ldots$	$[(69, 348)]$	$1$
169065.bc2	169065bh2	169065.bc	169065bh	$4$	$4$	\( 3^{2} \cdot 5 \cdot 13 \cdot 17^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 13^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$6.405298811$	$1$		$4$	$2064384$	$2.024296$	$39616946929/10989225$	$0.84706$	$3.98682$	$[1, -1, 0, -184725, 22096800]$	\(y^2+xy=x^3-x^2-184725x+22096800\)	2.6.0.a.1, 12.12.0-2.a.1.1, 68.12.0-2.a.1.1, 204.24.0.?, 260.12.0.?, $\ldots$	$[(2068, 91058)]$	$1$
212160.dl2	212160cx2	212160.dl	212160cx	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$26520$	$48$	$0$	$2.476888443$	$1$		$9$	$458752$	$1.098103$	$39616946929/10989225$	$0.84706$	$3.00684$	$[0, -1, 0, -4545, 86625]$	\(y^2=x^3-x^2-4545x+86625\)	2.6.0.a.1, 24.12.0-2.a.1.1, 136.12.0.?, 204.12.0.?, 408.24.0.?, $\ldots$	$[(72, 357)]$	$1$
212160.gg2	212160ei2	212160.gg	212160ei	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$26520$	$48$	$0$	$4.160038809$	$1$		$5$	$458752$	$1.098103$	$39616946929/10989225$	$0.84706$	$3.00684$	$[0, 1, 0, -4545, -86625]$	\(y^2=x^3+x^2-4545x-86625\)	2.6.0.a.1, 24.12.0-2.a.1.1, 136.12.0.?, 204.12.0.?, 408.24.0.?, $\ldots$	$[(-46, 165)]$	$1$
215475.r2	215475n2	215475.r	215475n	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13^{2} \cdot 17 \)	\( 3^{2} \cdot 5^{8} \cdot 13^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$13260$	$48$	$0$	$6.142762457$	$1$		$4$	$3612672$	$2.145576$	$39616946929/10989225$	$0.84706$	$4.02658$	$[1, 0, 0, -300063, -45676008]$	\(y^2+xy=x^3-300063x-45676008\)	2.6.0.a.1, 4.12.0-2.a.1.1, 204.24.0.?, 780.24.0.?, 4420.24.0.?, $\ldots$	$[(-172, 1010)]$	$1$
265200.i2	265200i2	265200.i	265200i	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 17 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{8} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$1.331430840$	$1$		$13$	$1376256$	$1.556248$	$39616946929/10989225$	$0.84706$	$3.39335$	$[0, -1, 0, -28408, 1339312]$	\(y^2=x^3-x^2-28408x+1339312\)	2.6.0.a.1, 52.12.0-2.a.1.1, 60.12.0-2.a.1.1, 204.12.0.?, 340.12.0.?, $\ldots$	$[(12, 1000)]$	$1$
281775.bj2	281775bj2	281775.bj	281775bj	$4$	$4$	\( 3 \cdot 5^{2} \cdot 13 \cdot 17^{2} \)	\( 3^{2} \cdot 5^{8} \cdot 13^{2} \cdot 17^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$7.899401459$	$1$		$2$	$6193152$	$2.279709$	$39616946929/10989225$	$0.84706$	$4.06877$	$[1, 1, 0, -513125, -102300000]$	\(y^2+xy=x^3+x^2-513125x-102300000\)	2.6.0.a.1, 20.12.0-2.a.1.1, 156.12.0.?, 204.12.0.?, 780.24.0.?, $\ldots$	$[(-1841/2, 50263/2)]$	$1$
401115.bk2	401115bk2	401115.bk	401115bk	$4$	$4$	\( 3 \cdot 5 \cdot 11^{2} \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 11^{6} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$145860$	$48$	$0$	$3.700774346$	$1$		$4$	$1146880$	$1.257330$	$39616946929/10989225$	$0.84706$	$3.00650$	$[1, 1, 0, -8593, 217672]$	\(y^2+xy=x^3+x^2-8593x+217672\)	2.6.0.a.1, 132.12.0.?, 204.12.0.?, 748.12.0.?, 780.12.0.?, $\ldots$	$[(136, 1192)]$	$1$
487305.dc2	487305dc2	487305.dc	487305dc	$4$	$4$	\( 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 17 \)	\( 3^{8} \cdot 5^{2} \cdot 7^{6} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$92820$	$48$	$0$	$2.907596611$	$1$		$6$	$2064384$	$1.580643$	$39616946929/10989225$	$0.84706$	$3.25806$	$[1, -1, 0, -31320, -1531629]$	\(y^2+xy=x^3-x^2-31320x-1531629\)	2.6.0.a.1, 28.12.0-2.a.1.1, 204.12.0.?, 780.12.0.?, 1428.24.0.?, $\ldots$	$[(-122, 741)]$	$1$

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