Elliptic curves over $\Q$ of conductor 23670

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

Results (31 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
23670.a1	23670d1	23670.a	23670d	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{18} \cdot 3^{8} \cdot 5^{3} \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2630$	$2$	$0$	$1$	$1$		$0$	$165888$	$1.683634$	$-947895115603862161/77561856000$	$0.95228$	$4.76420$	$1$	$[1, -1, 0, -184185, -30381075]$	\(y^2+xy=x^3-x^2-184185x-30381075\)	2630.2.0.?	$[ ]$	$1$
23670.b1	23670b1	23670.b	23670b	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{3} \cdot 3^{11} \cdot 5^{9} \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$31560$	$2$	$0$	$1$	$1$		$0$	$103680$	$1.539284$	$1145725929069119/998578125000$	$0.93487$	$4.09716$	$1$	$[1, -1, 0, 19620, 747576]$	\(y^2+xy=x^3-x^2+19620x+747576\)	31560.2.0.?	$[ ]$	$1$
23670.c1	23670c1	23670.c	23670c	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{2} \cdot 3^{16} \cdot 5^{7} \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2630$	$2$	$0$	$1$	$1$		$0$	$394240$	$2.050026$	$-89271531130775315041/4853089687500$	$0.97213$	$5.21547$	$1$	$[1, -1, 0, -837990, 295484656]$	\(y^2+xy=x^3-x^2-837990x+295484656\)	2630.2.0.?	$[ ]$	$1$
23670.d1	23670e1	23670.d	23670e	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{7} \cdot 3^{7} \cdot 5^{3} \cdot 263 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$31560$	$2$	$0$	$3.817261344$	$1$		$2$	$16128$	$0.595001$	$-1732323601/12624000$	$0.85277$	$3.02562$	$1$	$[1, -1, 0, -225, -4739]$	\(y^2+xy=x^3-x^2-225x-4739\)	31560.2.0.?	$[(125, 1319)]$	$1$
23670.e1	23670h1	23670.e	23670h	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{6} \cdot 3^{12} \cdot 5 \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$7890$	$16$	$0$	$1$	$1$		$0$	$18432$	$0.783470$	$-603136942849/61352640$	$0.86192$	$3.36369$	$1$	$[1, -1, 0, -1584, -25920]$	\(y^2+xy=x^3-x^2-1584x-25920\)	3.8.0-3.a.1.1, 2630.2.0.?, 7890.16.0.?	$[ ]$	$1$
23670.e2	23670h2	23670.e	23670h	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{2} \cdot 3^{8} \cdot 5^{3} \cdot 263^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$7890$	$16$	$0$	$1$	$1$		$2$	$55296$	$1.332775$	$140859621945791/81861511500$	$0.97581$	$3.88906$	$1$	$[1, -1, 0, 9756, 21708]$	\(y^2+xy=x^3-x^2+9756x+21708\)	3.8.0-3.a.1.2, 2630.2.0.?, 7890.16.0.?	$[ ]$	$1$
23670.f1	23670g4	23670.f	23670g	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{3} \cdot 3^{18} \cdot 5^{4} \cdot 263 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$31560$	$48$	$0$	$1$	$1$		$0$	$138240$	$1.678207$	$172668188300028049/698844915000$	$0.94399$	$4.59511$	$2$	$[1, -1, 0, -104409, -12913835]$	\(y^2+xy=x^3-x^2-104409x-12913835\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0-4.c.1.5, 120.24.0.?, $\ldots$	$[ ]$	$1$
23670.f2	23670g2	23670.f	23670g	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{6} \cdot 3^{12} \cdot 5^{2} \cdot 263^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$31560$	$48$	$0$	$1$	$1$		$2$	$69120$	$1.331633$	$139709488708369/80678721600$	$0.98585$	$3.88824$	$1$	$[1, -1, 0, -9729, 19453]$	\(y^2+xy=x^3-x^2-9729x+19453\)	2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 2104.12.0.?, $\ldots$	$[ ]$	$1$
23670.f3	23670g1	23670.f	23670g	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{12} \cdot 3^{9} \cdot 5 \cdot 263 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$31560$	$48$	$0$	$1$	$1$		$1$	$34560$	$0.985060$	$48743122863889/145428480$	$0.89449$	$3.78370$	$2$	$[1, -1, 0, -6849, 219325]$	\(y^2+xy=x^3-x^2-6849x+219325\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.6, 120.24.0.?, $\ldots$	$[ ]$	$1$
23670.f4	23670g3	23670.f	23670g	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{3} \cdot 3^{9} \cdot 5 \cdot 263^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$31560$	$48$	$0$	$1$	$1$		$0$	$138240$	$1.678207$	$8909781210821231/5167098605880$	$1.00619$	$4.30081$	$2$	$[1, -1, 0, 38871, 126373]$	\(y^2+xy=x^3-x^2+38871x+126373\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.1, 120.24.0.?, $\ldots$	$[ ]$	$1$
23670.g1	23670f4	23670.g	23670f	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2 \cdot 3^{8} \cdot 5^{8} \cdot 263 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$6312$	$48$	$0$	$1$	$1$		$0$	$114688$	$1.617678$	$1782692359777911889/1849218750$	$0.95524$	$4.82690$	$2$	$[1, -1, 0, -227349, -41667345]$	\(y^2+xy=x^3-x^2-227349x-41667345\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 24.24.0-8.p.1.5, 2104.24.0.?, $\ldots$	$[ ]$	$1$
23670.g2	23670f3	23670.g	23670f	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2 \cdot 3^{8} \cdot 5^{2} \cdot 263^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$6312$	$48$	$0$	$1$	$1$		$0$	$114688$	$1.617678$	$6267057803115409/2152957752450$	$0.93664$	$4.26588$	$2$	$[1, -1, 0, -34569, 1585683]$	\(y^2+xy=x^3-x^2-34569x+1585683\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 12.12.0-4.c.1.1, 24.24.0-8.k.1.1, $\ldots$	$[ ]$	$1$
23670.g3	23670f2	23670.g	23670f	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{2} \cdot 3^{10} \cdot 5^{4} \cdot 263^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.3	2Cs	$6312$	$48$	$0$	$1$	$1$		$2$	$57344$	$1.271105$	$445401126951409/14006722500$	$0.91030$	$4.00336$	$1$	$[1, -1, 0, -14319, -637767]$	\(y^2+xy=x^3-x^2-14319x-637767\)	2.6.0.a.1, 8.12.0.a.1, 12.12.0-2.a.1.1, 24.24.0-8.a.1.2, 1052.12.0.?, $\ldots$	$[ ]$	$1$
23670.g4	23670f1	23670.g	23670f	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{4} \cdot 3^{14} \cdot 5^{2} \cdot 263 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$6312$	$48$	$0$	$1$	$1$		$1$	$28672$	$0.924531$	$2691419471/690217200$	$0.92341$	$3.41509$	$2$	$[1, -1, 0, 261, -34155]$	\(y^2+xy=x^3-x^2+261x-34155\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 12.12.0-4.c.1.2, 24.24.0-8.p.1.8, $\ldots$	$[ ]$	$1$
23670.h1	23670i1	23670.h	23670i	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{30} \cdot 3^{12} \cdot 5^{13} \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2630$	$2$	$0$	$1$	$1$		$0$	$12579840$	$3.728424$	$399382556593519051068760271/251300413440000000000000$	$1.04317$	$6.73589$	$1$	$[1, -1, 0, 138080061, -184553949227]$	\(y^2+xy=x^3-x^2+138080061x-184553949227\)	2630.2.0.?	$[ ]$	$1$
23670.i1	23670a2	23670.i	23670a	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{7} \cdot 3^{9} \cdot 5^{6} \cdot 263^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$31560$	$12$	$0$	$1$	$1$		$0$	$145152$	$1.655041$	$282855913402707/138338000000$	$1.00847$	$4.28551$	$1$	$[1, -1, 0, -36924, -1065520]$	\(y^2+xy=x^3-x^2-36924x-1065520\)	2.3.0.a.1, 24.6.0.a.1, 10520.6.0.?, 15780.6.0.?, 31560.12.0.?	$[ ]$	$1$
23670.i2	23670a1	23670.i	23670a	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{14} \cdot 3^{9} \cdot 5^{3} \cdot 263 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$31560$	$12$	$0$	$1$	$1$		$1$	$72576$	$1.308468$	$42592647088467/538624000$	$0.96611$	$4.09753$	$1$	$[1, -1, 0, -19644, 1053008]$	\(y^2+xy=x^3-x^2-19644x+1053008\)	2.3.0.a.1, 24.6.0.d.1, 7890.6.0.?, 10520.6.0.?, 31560.12.0.?	$[ ]$	$1$
23670.j1	23670j1	23670.j	23670j	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{4} \cdot 3^{22} \cdot 5^{3} \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2630$	$2$	$0$	$1$	$1$		$0$	$245760$	$1.800953$	$36235446077848031/22642575246000$	$0.96764$	$4.44010$	$1$	$[1, -1, 0, 62046, -1695740]$	\(y^2+xy=x^3-x^2+62046x-1695740\)	2630.2.0.?	$[ ]$	$1$
23670.k1	23670p1	23670.k	23670p	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2 \cdot 3^{6} \cdot 5 \cdot 263 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10520$	$2$	$0$	$3.166516417$	$1$		$0$	$4800$	$-0.109209$	$1685159/2630$	$0.72358$	$2.13045$	$1$	$[1, -1, 1, 22, 47]$	\(y^2+xy+y=x^3-x^2+22x+47\)	10520.2.0.?	$[(-5/2, 33/2)]$	$1$
23670.l1	23670o1	23670.l	23670o	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{5} \cdot 3^{11} \cdot 5^{3} \cdot 263 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$31560$	$2$	$0$	$5.621671106$	$1$		$2$	$115200$	$1.537783$	$-1017261376770420361/255636000$	$0.95261$	$4.77120$	$1$	$[1, -1, 1, -188573, -31471419]$	\(y^2+xy+y=x^3-x^2-188573x-31471419\)	31560.2.0.?	$[(1193, 37356)]$	$1$
23670.m1	23670r1	23670.m	23670r	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2 \cdot 3^{11} \cdot 5 \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$31560$	$2$	$0$	$1$	$1$		$0$	$7680$	$0.358224$	$-594823321/639090$	$0.92537$	$2.76461$	$1$	$[1, -1, 1, -158, -1249]$	\(y^2+xy+y=x^3-x^2-158x-1249\)	31560.2.0.?	$[ ]$	$1$
23670.n1	23670m1	23670.n	23670m	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{21} \cdot 3^{9} \cdot 5 \cdot 263 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$31560$	$2$	$0$	$0.562580537$	$1$		$6$	$64512$	$1.315189$	$1576692510119/74459381760$	$1.05888$	$3.87884$	$1$	$[1, -1, 1, 2182, -352839]$	\(y^2+xy+y=x^3-x^2+2182x-352839\)	31560.2.0.?	$[(113, 1095)]$	$1$
23670.o1	23670l1	23670.o	23670l	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{3} \cdot 3^{6} \cdot 5^{7} \cdot 263 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10520$	$2$	$0$	$3.222039908$	$1$		$2$	$20160$	$0.806503$	$11836763639/164375000$	$0.88291$	$3.26863$	$1$	$[1, -1, 1, 427, 16197]$	\(y^2+xy+y=x^3-x^2+427x+16197\)	10520.2.0.?	$[(-15, 86)]$	$1$
23670.p1	23670n2	23670.p	23670n	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{11} \cdot 3^{9} \cdot 5^{8} \cdot 263^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6312$	$12$	$0$	$1.395743085$	$1$		$6$	$675840$	$2.409473$	$2738946892961807854201/1494050400000000$	$0.98511$	$5.55537$	$1$	$[1, -1, 1, -2623388, 1635352031]$	\(y^2+xy+y=x^3-x^2-2623388x+1635352031\)	2.3.0.a.1, 24.6.0.a.1, 1052.6.0.?, 6312.12.0.?	$[(853, 3781)]$	$1$
23670.p2	23670n1	23670.p	23670n	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{22} \cdot 3^{12} \cdot 5^{4} \cdot 263 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6312$	$12$	$0$	$0.697871542$	$1$		$9$	$337920$	$2.062901$	$-373809708740405881/502600826880000$	$0.96237$	$4.79104$	$1$	$[1, -1, 1, -135068, 34864607]$	\(y^2+xy+y=x^3-x^2-135068x+34864607\)	2.3.0.a.1, 24.6.0.d.1, 526.6.0.?, 6312.12.0.?	$[(-267, 7333)]$	$1$
23670.q1	23670q2	23670.q	23670q	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{15} \cdot 3^{11} \cdot 5 \cdot 263^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$31560$	$16$	$0$	$1$	$1$		$2$	$691200$	$2.309387$	$-575523643736199742921/724258262384640$	$0.97940$	$5.40070$	$1$	$[1, -1, 1, -1559633, 750894401]$	\(y^2+xy+y=x^3-x^2-1559633x+750894401\)	3.8.0-3.a.1.2, 31560.16.0.?	$[ ]$	$1$
23670.q2	23670q1	23670.q	23670q	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{5} \cdot 3^{21} \cdot 5^{3} \cdot 263 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$31560$	$16$	$0$	$1$	$1$		$0$	$230400$	$1.760080$	$2648635791002279/15095050164000$	$0.95316$	$4.39683$	$1$	$[1, -1, 1, 25942, 4777481]$	\(y^2+xy+y=x^3-x^2+25942x+4777481\)	3.8.0-3.a.1.1, 31560.16.0.?	$[ ]$	$1$
23670.r1	23670k2	23670.r	23670k	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{7} \cdot 3^{3} \cdot 5^{6} \cdot 263^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$31560$	$12$	$0$	$0.881194100$	$1$		$6$	$48384$	$1.105734$	$282855913402707/138338000000$	$1.00847$	$3.63105$	$1$	$[1, -1, 1, -4103, 40831]$	\(y^2+xy+y=x^3-x^2-4103x+40831\)	2.3.0.a.1, 24.6.0.a.1, 10520.6.0.?, 15780.6.0.?, 31560.12.0.?	$[(-7, 266)]$	$1$
23670.r2	23670k1	23670.r	23670k	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( 2^{14} \cdot 3^{3} \cdot 5^{3} \cdot 263 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$31560$	$12$	$0$	$1.762388200$	$1$		$5$	$24192$	$0.759161$	$42592647088467/538624000$	$0.96611$	$3.44308$	$1$	$[1, -1, 1, -2183, -38273]$	\(y^2+xy+y=x^3-x^2-2183x-38273\)	2.3.0.a.1, 24.6.0.d.1, 7890.6.0.?, 10520.6.0.?, 31560.12.0.?	$[(-25, 26)]$	$1$
23670.s1	23670s1	23670.s	23670s	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{21} \cdot 3^{6} \cdot 5 \cdot 263 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10520$	$2$	$0$	$0.524388684$	$1$		$4$	$40320$	$1.100950$	$-27458875316809/2757754880$	$0.89276$	$3.74261$	$1$	$[1, -1, 1, -5657, 178809]$	\(y^2+xy+y=x^3-x^2-5657x+178809\)	10520.2.0.?	$[(39, 108)]$	$1$
23670.t1	23670t1	23670.t	23670t	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 263 \)	\( - 2^{8} \cdot 3^{6} \cdot 5^{3} \cdot 263 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2630$	$2$	$0$	$0.264079932$	$1$		$8$	$15360$	$0.560350$	$1689410871/8416000$	$0.86286$	$2.96551$	$1$	$[1, -1, 1, 223, -3599]$	\(y^2+xy+y=x^3-x^2+223x-3599\)	2630.2.0.?	$[(31, 164)]$	$1$

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