Elliptic curves over $\Q$ of conductor 774

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (17 matches)

  Download displayed columns for results to

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
774.a1	774c1	774.a	774c	$1$	$1$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{2} \cdot 3^{25} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$516$	$2$	$0$	$1$	$1$		$0$	$6080$	$1.835733$	$-9500554530751882177/199908972324$	$1.04122$	$7.56056$	$[1, -1, 0, -397116, -96224252]$	\(y^2+xy=x^3-x^2-397116x-96224252\)	516.2.0.?	$[ ]$	$1$
774.b1	774e1	774.b	774e	$2$	$2$	\( 2 \cdot 3^{2} \cdot 43 \)	\( 2^{2} \cdot 3^{7} \cdot 43 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$1032$	$12$	$0$	$0.318104051$	$1$		$11$	$96$	$-0.240190$	$912673/516$	$0.90862$	$3.05429$	$[1, -1, 0, -18, 0]$	\(y^2+xy=x^3-x^2-18x\)	2.3.0.a.1, 8.6.0.d.1, 258.6.0.?, 1032.12.0.?	$[(6, 6)]$	$1$
774.b2	774e2	774.b	774e	$2$	$2$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2 \cdot 3^{8} \cdot 43^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$1032$	$12$	$0$	$0.636208103$	$1$		$6$	$192$	$0.106383$	$56181887/33282$	$0.96315$	$3.67368$	$[1, -1, 0, 72, -54]$	\(y^2+xy=x^3-x^2+72x-54\)	2.3.0.a.1, 8.6.0.a.1, 516.6.0.?, 1032.12.0.?	$[(3, 12)]$	$1$
774.c1	774d2	774.c	774d	$2$	$7$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{2} \cdot 3^{7} \cdot 43^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$3612$	$96$	$2$	$0.144128547$	$1$		$8$	$9408$	$1.968227$	$-23769846831649063249/3261823333284$	$1.04406$	$7.69846$	$[1, -1, 0, -539109, 152510121]$	\(y^2+xy=x^3-x^2-539109x+152510121\)	7.24.0.a.2, 21.48.0-7.a.2.2, 516.2.0.?, 1204.48.0.?, 3612.96.2.?	$[(-564, 16923)]$	$1$
774.c2	774d1	774.c	774d	$2$	$7$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{14} \cdot 3^{13} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.1	7B.6.1	$3612$	$96$	$2$	$1.008899832$	$1$		$4$	$1344$	$0.995273$	$444369620591/1540767744$	$0.99664$	$5.26482$	$[1, -1, 0, 1431, -46899]$	\(y^2+xy=x^3-x^2+1431x-46899\)	7.24.0.a.1, 21.48.0-7.a.1.2, 516.2.0.?, 1204.48.0.?, 3612.96.2.?	$[(66, 543)]$	$1$
774.d1	774b3	774.d	774b	$4$	$4$	\( 2 \cdot 3^{2} \cdot 43 \)	\( 2^{3} \cdot 3^{7} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1032$	$48$	$0$	$1$	$1$		$0$	$1920$	$1.042383$	$18440127492397057/1032$	$1.01875$	$6.62174$	$[1, -1, 0, -49536, 4255960]$	\(y^2+xy=x^3-x^2-49536x+4255960\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.7, 172.12.0.?, $\ldots$	$[ ]$	$1$
774.d2	774b2	774.d	774b	$4$	$4$	\( 2 \cdot 3^{2} \cdot 43 \)	\( 2^{6} \cdot 3^{8} \cdot 43^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.4	2Cs	$1032$	$48$	$0$	$1$	$1$		$2$	$960$	$0.695809$	$4502751117697/1065024$	$1.04479$	$5.37127$	$[1, -1, 0, -3096, 67072]$	\(y^2+xy=x^3-x^2-3096x+67072\)	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.2, 172.12.0.?, $\ldots$	$[ ]$	$1$
774.d3	774b4	774.d	774b	$4$	$4$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{3} \cdot 3^{10} \cdot 43^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.16	2B	$1032$	$48$	$0$	$1$	$1$		$0$	$1920$	$1.042383$	$-3107661785857/2215383048$	$0.98806$	$5.43622$	$[1, -1, 0, -2736, 82984]$	\(y^2+xy=x^3-x^2-2736x+82984\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 12.12.0-4.c.1.1, 24.24.0-8.d.1.1, $\ldots$	$[ ]$	$1$
774.d4	774b1	774.d	774b	$4$	$4$	\( 2 \cdot 3^{2} \cdot 43 \)	\( 2^{12} \cdot 3^{7} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1032$	$48$	$0$	$1$	$1$		$1$	$480$	$0.349236$	$1532808577/528384$	$0.93069$	$4.17075$	$[1, -1, 0, -216, 832]$	\(y^2+xy=x^3-x^2-216x+832\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.8, $\ldots$	$[ ]$	$1$
774.e1	774a2	774.e	774a	$2$	$3$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{12} \cdot 3^{9} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$516$	$16$	$0$	$1$	$1$		$0$	$576$	$0.680293$	$-37226247219/176128$	$0.95713$	$5.14704$	$[1, -1, 0, -1878, -30988]$	\(y^2+xy=x^3-x^2-1878x-30988\)	3.8.0-3.a.1.1, 516.16.0.?	$[ ]$	$1$
774.e2	774a1	774.e	774a	$2$	$3$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{3} \cdot 43^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$516$	$16$	$0$	$1$	$1$		$2$	$192$	$0.130987$	$751089429/1272112$	$0.95534$	$3.66660$	$[1, -1, 0, 57, -243]$	\(y^2+xy=x^3-x^2+57x-243\)	3.8.0-3.a.1.2, 516.16.0.?	$[ ]$	$1$
774.f1	774f1	774.f	774f	$2$	$3$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{12} \cdot 3^{3} \cdot 43 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$516$	$16$	$0$	$0.418722863$	$1$		$14$	$192$	$0.130987$	$-37226247219/176128$	$0.95713$	$4.15605$	$[1, -1, 1, -209, 1217]$	\(y^2+xy+y=x^3-x^2-209x+1217\)	3.8.0-3.a.1.2, 516.16.0.?	$[(9, -8)]$	$1$
774.f2	774f2	774.f	774f	$2$	$3$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{4} \cdot 3^{9} \cdot 43^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$516$	$16$	$0$	$0.139574287$	$1$		$6$	$576$	$0.680293$	$751089429/1272112$	$0.95534$	$4.65760$	$[1, -1, 1, 511, 6049]$	\(y^2+xy+y=x^3-x^2+511x+6049\)	3.8.0-3.a.1.1, 516.16.0.?	$[(109, 1106)]$	$1$
774.g1	774g1	774.g	774g	$1$	$1$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{6} \cdot 3^{7} \cdot 43 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$516$	$2$	$0$	$0.067708442$	$1$		$12$	$192$	$-0.016863$	$1685159/8256$	$0.89017$	$3.44872$	$[1, -1, 1, 22, 105]$	\(y^2+xy+y=x^3-x^2+22x+105\)	516.2.0.?	$[(-1, 9)]$	$1$
774.h1	774h1	774.h	774h	$2$	$2$	\( 2 \cdot 3^{2} \cdot 43 \)	\( 2^{14} \cdot 3^{13} \cdot 43 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$1032$	$12$	$0$	$1$	$1$		$1$	$1568$	$1.200113$	$778510269523657/1540767744$	$1.00479$	$6.14593$	$[1, -1, 1, -17249, -866127]$	\(y^2+xy+y=x^3-x^2-17249x-866127\)	2.3.0.a.1, 8.6.0.d.1, 258.6.0.?, 1032.12.0.?	$[ ]$	$1$
774.h2	774h2	774.h	774h	$2$	$2$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{7} \cdot 3^{20} \cdot 43^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$1032$	$12$	$0$	$1$	$1$		$0$	$3136$	$1.546686$	$-230042158153417/1131994839168$	$1.03167$	$6.30115$	$[1, -1, 1, -11489, -1458255]$	\(y^2+xy+y=x^3-x^2-11489x-1458255\)	2.3.0.a.1, 8.6.0.a.1, 516.6.0.?, 1032.12.0.?	$[ ]$	$1$
774.i1	774i1	774.i	774i	$1$	$1$	\( 2 \cdot 3^{2} \cdot 43 \)	\( - 2^{2} \cdot 3^{11} \cdot 43 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$516$	$2$	$0$	$1$	$1$		$0$	$320$	$0.170630$	$-338608873/41796$	$0.90085$	$3.97280$	$[1, -1, 1, -131, -601]$	\(y^2+xy+y=x^3-x^2-131x-601\)	516.2.0.?	$[ ]$	$1$

  Download displayed columns for results to