Elliptic curves over $\Q$ of conductor 343230

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

Results (16 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
343230.a1	343230a1	343230.a	343230a	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{2} \cdot 3 \cdot 5^{3} \cdot 17^{5} \cdot 673 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$343230$	$2$	$0$	$0.143170972$	$1$		$8$	$1743360$	$1.108175$	$-44497719675947881/1433345641500$	$0.85845$	$3.01176$	$1$	$[1, 1, 0, -7382, 247776]$	\(y^2+xy=x^3+x^2-7382x+247776\)	343230.2.0.?	$[(142, 1374)]$	$1$
343230.b1	343230b1	343230.b	343230b	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( 2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 17^{2} \cdot 673 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.3	2B	$1372920$	$48$	$0$	$3.066708858$	$1$		$3$	$1505280$	$1.411455$	$114799830128267551561/100827244800$	$0.90148$	$3.62382$	$2$	$[1, 1, 0, -101252, -12443184]$	\(y^2+xy=x^3+x^2-101252x-12443184\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 1346.6.0.?, 2692.12.0.?, $\ldots$	$[(392, 2684)]$	$1$
343230.b2	343230b2	343230.b	343230b	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{4} \cdot 3^{2} \cdot 5^{4} \cdot 17^{4} \cdot 673^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.5	2B	$1372920$	$48$	$0$	$1.533354429$	$1$		$4$	$3010560$	$1.758028$	$-112368201472638033481/3404617470810000$	$0.90192$	$3.62614$	$1$	$[1, 1, 0, -100532, -12627936]$	\(y^2+xy=x^3+x^2-100532x-12627936\)	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 2692.12.0.?, 16152.24.0.?, $\ldots$	$[(728, 16976)]$	$1$
343230.c1	343230c1	343230.c	343230c	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{16} \cdot 3^{3} \cdot 5 \cdot 17 \cdot 673 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$343230$	$2$	$0$	$11.27028995$	$1$		$0$	$473088$	$0.987400$	$-38875878721405081/101222645760$	$0.85695$	$2.99727$	$1$	$[1, 1, 0, -7057, -231659]$	\(y^2+xy=x^3+x^2-7057x-231659\)	343230.2.0.?	$[(1173026/41, 1237884487/41)]$	$1$
343230.d1	343230d1	343230.d	343230d	$2$	$3$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{6} \cdot 3^{15} \cdot 5 \cdot 17^{3} \cdot 673 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$343230$	$16$	$0$	$1$	$1$		$2$	$3939840$	$1.902399$	$-868100230514093335849/15182057344397760$	$0.91130$	$3.78488$	$1$	$[1, 0, 1, -198739, 34596206]$	\(y^2+xy+y=x^3-198739x+34596206\)	3.8.0-3.a.1.2, 343230.16.0.?	$[ ]$	$1$
343230.d2	343230d2	343230.d	343230d	$2$	$3$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{18} \cdot 3^{5} \cdot 5^{3} \cdot 17 \cdot 673^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$343230$	$16$	$0$	$1$	$1$		$0$	$11819520$	$2.451706$	$50892531298731620140391/41262004549287936000$	$0.94203$	$4.10194$	$1$	$[1, 0, 1, 772046, 165408452]$	\(y^2+xy+y=x^3+772046x+165408452\)	3.8.0-3.a.1.1, 343230.16.0.?	$[ ]$	$1$
343230.e1	343230e1	343230.e	343230e	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{6} \cdot 3^{3} \cdot 5^{5} \cdot 17 \cdot 673 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$343230$	$2$	$0$	$0.476152800$	$1$		$6$	$339840$	$0.751877$	$-3885442650361/61781400000$	$0.83824$	$2.53703$	$1$	$[1, 0, 1, -328, -12202]$	\(y^2+xy+y=x^3-328x-12202\)	343230.2.0.?	$[(49, 275)]$	$1$
343230.f1	343230f1	343230.f	343230f	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{2} \cdot 3^{5} \cdot 5 \cdot 17 \cdot 673 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$343230$	$2$	$0$	$2.888186510$	$1$		$2$	$102400$	$0.170426$	$-10779215329/55603260$	$0.86690$	$1.99235$	$1$	$[1, 1, 1, -46, 359]$	\(y^2+xy+y=x^3+x^2-46x+359\)	343230.2.0.?	$[(21, 85)]$	$1$
343230.g1	343230g1	343230.g	343230g	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{4} \cdot 3^{9} \cdot 5 \cdot 17 \cdot 673 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$343230$	$2$	$0$	$1$	$1$		$0$	$253440$	$0.646821$	$6549699311/18015456240$	$0.86749$	$2.43752$	$1$	$[1, 1, 1, 39, -6441]$	\(y^2+xy+y=x^3+x^2+39x-6441\)	343230.2.0.?	$[ ]$	$1$
343230.h1	343230h1	343230.h	343230h	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{2} \cdot 3 \cdot 5^{9} \cdot 17 \cdot 673 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$343230$	$2$	$0$	$46.89021832$	$1$		$0$	$1852416$	$1.550047$	$-791917563504767668129/268148437500$	$0.91057$	$3.77533$	$1$	$[1, 1, 1, -192746, -32650957]$	\(y^2+xy+y=x^3+x^2-192746x-32650957\)	343230.2.0.?	$[(317785224190444891549/191522631, 5627561463365262825957444915167/191522631)]$	$1$
343230.i1	343230i1	343230.i	343230i	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{14} \cdot 3^{4} \cdot 5^{2} \cdot 17^{2} \cdot 673 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$2692$	$2$	$0$	$0.158423334$	$1$		$28$	$759808$	$1.144350$	$-1991292834850129/6452943667200$	$0.86221$	$2.91183$	$1$	$[1, 0, 0, -2621, 132465]$	\(y^2+xy=x^3-2621x+132465\)	2692.2.0.?	$[(-14, 415), (-62, 271)]$	$1$
343230.j1	343230j1	343230.j	343230j	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{17} \cdot 3^{5} \cdot 5 \cdot 17^{2} \cdot 673 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$80760$	$2$	$0$	$0.237702990$	$1$		$8$	$1433440$	$1.267851$	$113597901646991/30974129602560$	$0.90013$	$3.02183$	$1$	$[1, 0, 0, 1009, -267399]$	\(y^2+xy=x^3+1009x-267399\)	80760.2.0.?	$[(118, 1165)]$	$1$
343230.k1	343230k1	343230.k	343230k	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( 2^{2} \cdot 3^{4} \cdot 5^{4} \cdot 17 \cdot 673 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$91528$	$12$	$0$	$1$	$1$		$1$	$645120$	$1.026604$	$793819571525004961/2316802500$	$0.94405$	$3.23357$	$1$	$[1, 0, 0, -19290, 1029600]$	\(y^2+xy=x^3-19290x+1029600\)	2.3.0.a.1, 8.6.0.d.1, 22882.6.0.?, 91528.12.0.?	$[ ]$	$1$
343230.k2	343230k2	343230.k	343230k	$2$	$2$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2 \cdot 3^{8} \cdot 5^{2} \cdot 17^{2} \cdot 673^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$91528$	$12$	$0$	$1$	$1$		$0$	$1290240$	$1.373177$	$-763353972260328961/42940590592050$	$0.94498$	$3.23778$	$1$	$[1, 0, 0, -19040, 1057650]$	\(y^2+xy=x^3-19040x+1057650\)	2.3.0.a.1, 8.6.0.a.1, 45764.6.0.?, 91528.12.0.?	$[ ]$	$1$
343230.l1	343230l2	343230.l	343230l	$2$	$7$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 673^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$2402610$	$96$	$2$	$1$	$49$	$7$	$0$	$337446144$	$4.240509$	$-537892346392757834815139433407447761/63783099740879053154940$	$1.01188$	$6.45473$	$1$	$[1, 0, 0, -16943009365, -848857250127235]$	\(y^2+xy=x^3-16943009365x-848857250127235\)	7.48.0-7.a.2.2, 343230.2.0.?, 2402610.96.2.?	$[ ]$	$1$
343230.l2	343230l1	343230.l	343230l	$2$	$7$	\( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 673 \)	\( - 2^{14} \cdot 3^{7} \cdot 5^{7} \cdot 17^{7} \cdot 673 \)	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$2402610$	$96$	$2$	$1$	$1$		$6$	$48206592$	$3.267551$	$309877627207229469173251439/773065454327965440000000$	$0.97324$	$4.87955$	$1$	$[1, 0, 0, 14097935, -37071642775]$	\(y^2+xy=x^3+14097935x-37071642775\)	7.48.0-7.a.1.2, 343230.2.0.?, 2402610.96.2.?	$[ ]$	$1$

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