Elliptic curves over $\Q$ of conductor 1365

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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
1365.a1	1365b5	1365.a	1365b	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{6} \cdot 5 \cdot 7 \cdot 13^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$21840$	$192$	$1$	$1$	$1$		$0$	$6144$	$1.605856$	$282352188585428161201/20813369346315$	$0.99865$	$6.52310$	$[1, 1, 1, -136675, -19504018]$	\(y^2+xy+y=x^3+x^2-136675x-19504018\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 120.48.0.?, 140.24.0.?, $\ldots$	$[ ]$
1365.a2	1365b4	1365.a	1365b	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{3} \cdot 5^{2} \cdot 7^{8} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$21840$	$192$	$1$	$1$	$1$		$2$	$3072$	$1.259283$	$11372424889583066401/50586128775$	$0.98653$	$6.07816$	$[1, 1, 1, -46850, 3883592]$	\(y^2+xy+y=x^3+x^2-46850x+3883592\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 120.48.0.?, 156.24.0.?, $\ldots$	$[ ]$
1365.a3	1365b3	1365.a	1365b	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{12} \cdot 5^{2} \cdot 7^{2} \cdot 13^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.6	2Cs	$10920$	$192$	$1$	$1$	$1$		$2$	$3072$	$1.259283$	$83339496416030401/18593645841225$	$0.97073$	$5.39717$	$[1, 1, 1, -9100, -265708]$	\(y^2+xy+y=x^3+x^2-9100x-265708\)	2.6.0.a.1, 4.24.0-4.b.1.1, 120.48.0.?, 140.48.0.?, 168.48.0.?, $\ldots$	$[ ]$
1365.a4	1365b2	1365.a	1365b	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{6} \cdot 5^{4} \cdot 7^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.5	2Cs	$10920$	$192$	$1$	$1$	$1$		$6$	$1536$	$0.912708$	$2912015927948401/184878500625$	$0.94885$	$4.93255$	$[1, 1, 1, -2975, 57692]$	\(y^2+xy+y=x^3+x^2-2975x+57692\)	2.6.0.a.1, 4.24.0-4.b.1.3, 120.48.0.?, 156.48.0.?, 168.48.0.?, $\ldots$	$[ ]$
1365.a5	1365b1	1365.a	1365b	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 3^{3} \cdot 5^{8} \cdot 7^{2} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$21840$	$192$	$1$	$1$	$1$		$3$	$768$	$0.566135$	$373092501599/6718359375$	$0.94544$	$4.16270$	$[1, 1, 1, 150, 3942]$	\(y^2+xy+y=x^3+x^2+150x+3942\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 78.6.0.?, 156.24.0.?, $\ldots$	$[ ]$
1365.a6	1365b6	1365.a	1365b	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 3^{24} \cdot 5 \cdot 7 \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$21840$	$192$	$1$	$1$	$4$	$2$	$0$	$6144$	$1.605856$	$949279533867428399/1670570708285115$	$0.99398$	$5.83300$	$[1, 1, 1, 20475, -1602498]$	\(y^2+xy+y=x^3+x^2+20475x-1602498\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 70.6.0.a.1, 140.24.0.?, $\ldots$	$[ ]$
1365.b1	1365d3	1365.b	1365d	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{12} \cdot 5^{4} \cdot 7^{3} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$0.131585550$	$1$		$14$	$3456$	$1.257187$	$1559802282754777489/1481059636875$	$0.97830$	$5.80297$	$[1, 0, 0, -24161, 1442310]$	\(y^2+xy=x^3-24161x+1442310\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.1, 52.12.0-4.c.1.2, 120.12.0.?, $\ldots$	$[(73, 226)]$
1365.b2	1365d2	1365.b	1365d	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{6} \cdot 5^{2} \cdot 7^{6} \cdot 13^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$5460$	$48$	$0$	$0.263171101$	$1$		$20$	$1728$	$0.910613$	$718576775407009/362361861225$	$0.96651$	$4.73871$	$[1, 0, 0, -1866, 10971]$	\(y^2+xy=x^3-1866x+10971\)	2.6.0.a.1, 28.12.0-2.a.1.1, 52.12.0-2.a.1.1, 60.12.0-2.a.1.1, 364.24.0.?, $\ldots$	$[(3, 72)]$
1365.b3	1365d1	1365.b	1365d	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{3} \cdot 5 \cdot 7^{3} \cdot 13^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$0.526342202$	$1$		$7$	$864$	$0.564040$	$117713838907729/1322517105$	$0.92830$	$4.48811$	$[1, 0, 0, -1021, -12520]$	\(y^2+xy=x^3-1021x-12520\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 60.12.0-4.c.1.2, 104.12.0.?, $\ldots$	$[(-19, 20)]$
1365.b4	1365d4	1365.b	1365d	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 3^{3} \cdot 5 \cdot 7^{12} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$0.526342202$	$1$		$6$	$3456$	$1.257187$	$36472485598112591/24291459037755$	$1.07485$	$5.28270$	$[1, 0, 0, 6909, 86436]$	\(y^2+xy=x^3+6909x+86436\)	2.3.0.a.1, 4.6.0.c.1, 52.12.0-4.c.1.1, 56.12.0-4.c.1.5, 60.12.0-4.c.1.1, $\ldots$	$[(0, 294)]$
1365.c1	1365a3	1365.c	1365a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{5} \cdot 5^{4} \cdot 7^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$0$	$1920$	$1.022413$	$531301262949272089/4740474375$	$0.97353$	$5.65378$	$[1, 1, 0, -16873, 836602]$	\(y^2+xy=x^3+x^2-16873x+836602\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 52.12.0-4.c.1.2, 156.24.0.?, $\ldots$	$[ ]$
1365.c2	1365a2	1365.c	1365a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$5460$	$48$	$0$	$1$	$1$		$2$	$960$	$0.675840$	$138742439989609/12224619225$	$0.93130$	$4.51088$	$[1, 1, 0, -1078, 12103]$	\(y^2+xy=x^3+x^2-1078x+12103\)	2.6.0.a.1, 12.12.0-2.a.1.1, 52.12.0-2.a.1.1, 140.12.0.?, 156.24.0.?, $\ldots$	$[ ]$
1365.c3	1365a1	1365.c	1365a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{5} \cdot 5 \cdot 7 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$480$	$0.329267$	$1408317602329/242911305$	$0.90102$	$3.87502$	$[1, 1, 0, -233, -1248]$	\(y^2+xy=x^3+x^2-233x-1248\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 104.12.0.?, 140.12.0.?, $\ldots$	$[ ]$
1365.c4	1365a4	1365.c	1365a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 3^{20} \cdot 5 \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$4$	$2$	$0$	$1920$	$1.022413$	$189425802193991/1586486902455$	$0.97102$	$4.91427$	$[1, 1, 0, 1197, 58968]$	\(y^2+xy=x^3+x^2+1197x+58968\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 52.12.0-4.c.1.1, 140.12.0.?, $\ldots$	$[ ]$
1365.d1	1365c3	1365.d	1365c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{2} \cdot 5^{4} \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$3640$	$48$	$0$	$1$	$4$	$2$	$0$	$1024$	$0.563480$	$9219915604149769/511875$	$0.95368$	$5.09220$	$[1, 0, 1, -4369, -111499]$	\(y^2+xy+y=x^3-4369x-111499\)	2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 40.12.0-4.c.1.5, 52.12.0-4.c.1.1, $\ldots$	$[ ]$
1365.d2	1365c2	1365.d	1365c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$1820$	$48$	$0$	$1$	$1$		$2$	$512$	$0.216907$	$2263054145689/16769025$	$0.89990$	$3.94072$	$[1, 0, 1, -274, -1753]$	\(y^2+xy+y=x^3-274x-1753\)	2.6.0.a.1, 20.12.0-2.a.1.1, 28.12.0-2.a.1.1, 52.12.0-2.a.1.1, 140.24.0.?, $\ldots$	$[ ]$
1365.d3	1365c4	1365.d	1365c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 3^{8} \cdot 5 \cdot 7 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$3640$	$48$	$0$	$1$	$1$		$0$	$1024$	$0.563480$	$-105756712489/6558605235$	$0.95735$	$4.16518$	$[1, 0, 1, -99, -3923]$	\(y^2+xy+y=x^3-99x-3923\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 28.12.0-4.c.1.1, 70.6.0.a.1, $\ldots$	$[ ]$
1365.d4	1365c1	1365.d	1365c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{2} \cdot 5 \cdot 7^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$3640$	$48$	$0$	$1$	$1$		$1$	$256$	$-0.129667$	$2565726409/1404585$	$1.03680$	$3.00122$	$[1, 0, 1, -29, 11]$	\(y^2+xy+y=x^3-29x+11\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 52.12.0-4.c.1.2, 56.12.0-4.c.1.5, $\ldots$	$[ ]$
1365.e1	1365e4	1365.e	1365e	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3 \cdot 5 \cdot 7 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$0$	$384$	$0.255499$	$19790357598649/2998905$	$0.91596$	$4.24111$	$[1, 0, 1, -564, 5101]$	\(y^2+xy+y=x^3-564x+5101\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 104.12.0.?, 140.12.0.?, $\ldots$	$[ ]$
1365.e2	1365e3	1365.e	1365e	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3 \cdot 5^{4} \cdot 7^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$0$	$384$	$0.255499$	$1408317602329/58524375$	$0.89699$	$3.87502$	$[1, 0, 1, -234, -1343]$	\(y^2+xy+y=x^3-234x-1343\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 52.12.0-4.c.1.1, 156.24.0.?, $\ldots$	$[ ]$
1365.e3	1365e2	1365.e	1365e	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$5460$	$48$	$0$	$1$	$1$		$2$	$192$	$-0.091075$	$6321363049/1863225$	$0.99851$	$3.12612$	$[1, 0, 1, -39, 61]$	\(y^2+xy+y=x^3-39x+61\)	2.6.0.a.1, 12.12.0-2.a.1.1, 52.12.0-2.a.1.1, 140.12.0.?, 156.24.0.?, $\ldots$	$[ ]$
1365.e4	1365e1	1365.e	1365e	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 3^{4} \cdot 5 \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$10920$	$48$	$0$	$1$	$1$		$1$	$96$	$-0.437648$	$30080231/36855$	$0.80519$	$2.40067$	$[1, 0, 1, 6, 7]$	\(y^2+xy+y=x^3+6x+7\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 52.12.0-4.c.1.2, 140.12.0.?, $\ldots$	$[ ]$
1365.f1	1365f3	1365.f	1365f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{4} \cdot 5^{8} \cdot 7 \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$2184$	$48$	$0$	$1$	$1$		$2$	$768$	$0.546124$	$24190225473961/2879296875$	$0.92052$	$4.26892$	$[1, 0, 1, -603, 5023]$	\(y^2+xy+y=x^3-603x+5023\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 364.24.0.?, 2184.48.0.?	$[ ]$
1365.f2	1365f2	1365.f	1365f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3^{2} \cdot 5^{4} \cdot 7^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1092$	$48$	$0$	$1$	$1$		$2$	$384$	$0.199550$	$355045312441/46580625$	$0.88810$	$3.68415$	$[1, 0, 1, -148, -619]$	\(y^2+xy+y=x^3-148x-619\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 364.24.0.?, 1092.48.0.?	$[ ]$
1365.f3	1365f1	1365.f	1365f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( 3 \cdot 5^{2} \cdot 7 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$2184$	$48$	$0$	$1$	$4$	$2$	$1$	$192$	$-0.147023$	$320153881321/6825$	$0.88340$	$3.66982$	$[1, 0, 1, -143, -667]$	\(y^2+xy+y=x^3-143x-667\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$	$[ ]$
1365.f4	1365f4	1365.f	1365f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 13 \)	\( - 3 \cdot 5^{2} \cdot 7^{4} \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$2184$	$48$	$0$	$1$	$1$		$0$	$768$	$0.546124$	$1301812981559/5143122075$	$0.93061$	$4.10827$	$[1, 0, 1, 227, -3169]$	\(y^2+xy+y=x^3+227x-3169\)	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 728.24.0.?, $\ldots$	$[ ]$

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