Elliptic curves over $\Q$ of conductor 1155

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (41 matches)

 

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
1155.a1	1155g1	1155.a	1155g	$1$	$1$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3 \cdot 5^{3} \cdot 7 \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.143125989$	$1$		$6$	$144$	$-0.465187$	$-4096/28875$	$[0, -1, 1, 0, 8]$	\(y^2+y=x^3-x^2+8\)
1155.b1	1155i1	1155.b	1155i	$1$	$1$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{7} \cdot 5 \cdot 7 \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.077057682$	$1$		$10$	$336$	$-0.003631$	$-222985990144/841995$	$[0, 1, 1, -126, 506]$	\(y^2+y=x^3+x^2-126x+506\)
1155.c1	1155n2	1155.c	1155n	$2$	$5$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3 \cdot 5 \cdot 7 \cdot 11^{15} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.3	5B.1.2	$0.866250978$	$1$		$0$	$30000$	$2.064484$	$-2126464142970105856/438611057788643355$	$[0, 1, 1, -26790, -31917424]$	\(y^2+y=x^3+x^2-26790x-31917424\)
1155.c2	1155n1	1155.c	1155n	$2$	$5$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{5} \cdot 5^{5} \cdot 7^{5} \cdot 11^{3} \)	$1$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.1	5B.1.1	$0.173250195$	$1$		$30$	$6000$	$1.259766$	$-79028701534867456/16987307596875$	$[0, 1, 1, -8940, 378056]$	\(y^2+y=x^3+x^2-8940x+378056\)
1155.d1	1155a3	1155.d	1155a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3 \cdot 5 \cdot 7^{4} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1.011716055$	$1$		$4$	$384$	$0.270145$	$75627935783569/396165$	$[1, 1, 1, -881, 9698]$	\(y^2+xy+y=x^3+x^2-881x+9698\)
1155.d2	1155a2	1155.d	1155a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$0.505858027$	$1$		$14$	$192$	$-0.076428$	$19443408769/1334025$	$[1, 1, 1, -56, 128]$	\(y^2+xy+y=x^3+x^2-56x+128\)
1155.d3	1155a1	1155.d	1155a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5 \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1.011716055$	$1$		$5$	$96$	$-0.423002$	$148035889/31185$	$[1, 1, 1, -11, -16]$	\(y^2+xy+y=x^3+x^2-11x-16\)
1155.d4	1155a4	1155.d	1155a	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3 \cdot 5^{4} \cdot 7 \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1.011716055$	$1$		$4$	$384$	$0.270145$	$12994449551/192163125$	$[1, 1, 1, 49, 674]$	\(y^2+xy+y=x^3+x^2+49x+674\)
1155.e1	1155e5	1155.e	1155e	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{8} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$1.700180605$	$1$		$4$	$2048$	$1.013866$	$257260669489908001/14267882475$	$[1, 1, 1, -13250, -592540]$	\(y^2+xy+y=x^3+x^2-13250x-592540\)
1155.e2	1155e3	1155.e	1155e	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5^{4} \cdot 7^{4} \cdot 11^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.6	2Cs	$0.850090302$	$1$		$12$	$1024$	$0.667294$	$74093292126001/14707625625$	$[1, 1, 1, -875, -8440]$	\(y^2+xy+y=x^3+x^2-875x-8440\)
1155.e3	1155e2	1155.e	1155e	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11^{4} \)	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.5	2Cs	$1.700180605$	$1$		$14$	$512$	$0.320720$	$2177286259681/161417025$	$[1, 1, 1, -270, 1482]$	\(y^2+xy+y=x^3+x^2-270x+1482\)
1155.e4	1155e1	1155.e	1155e	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3 \cdot 5 \cdot 7 \cdot 11^{2} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$3.400361211$	$1$		$5$	$256$	$-0.025854$	$2058561081361/12705$	$[1, 1, 1, -265, 1550]$	\(y^2+xy+y=x^3+x^2-265x+1550\)
1155.e5	1155e4	1155.e	1155e	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3 \cdot 5 \cdot 7 \cdot 11^{8} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$3.400361211$	$1$		$4$	$1024$	$0.667294$	$1833318007919/22507682505$	$[1, 1, 1, 255, 7152]$	\(y^2+xy+y=x^3+x^2+255x+7152\)
1155.e6	1155e6	1155.e	1155e	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$0.425045151$	$1$		$10$	$2048$	$1.013866$	$666688497209279/1381398046875$	$[1, 1, 1, 1820, -47248]$	\(y^2+xy+y=x^3+x^2+1820x-47248\)
1155.f1	1155m5	1155.f	1155m	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{3} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$1$	$4$	$2$	$0$	$7680$	$1.899137$	$3135316978843283198764801/571725$	$[1, 0, 0, -3049200, -2049655293]$	\(y^2+xy=x^3-3049200x-2049655293\)
1155.f2	1155m3	1155.f	1155m	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{6} \cdot 5^{4} \cdot 7^{2} \cdot 11^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.6	2Cs	$1$	$1$		$2$	$3840$	$1.552563$	$765458482133960722801/326869475625$	$[1, 0, 0, -190575, -32037768]$	\(y^2+xy=x^3-190575x-32037768\)
1155.f3	1155m6	1155.f	1155m	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{3} \cdot 5^{8} \cdot 7 \cdot 11^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$1$	$1$		$0$	$7680$	$1.899137$	$-754127868744065783521/15825714261328125$	$[1, 0, 0, -189630, -32370975]$	\(y^2+xy=x^3-189630x-32370975\)
1155.f4	1155m4	1155.f	1155m	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{24} \cdot 5 \cdot 7^{2} \cdot 11 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$1$	$1$		$2$	$3840$	$1.552563$	$1821931919215868881/761147600816295$	$[1, 0, 0, -25445, 821730]$	\(y^2+xy=x^3-25445x+821730\)
1155.f5	1155m2	1155.f	1155m	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{12} \cdot 5^{2} \cdot 7^{4} \cdot 11^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.5	2Cs	$1$	$1$		$6$	$1920$	$1.205990$	$189674274234120481/3859869269025$	$[1, 0, 0, -11970, -496125]$	\(y^2+xy=x^3-11970x-496125\)
1155.f6	1155m1	1155.f	1155m	$6$	$8$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{6} \cdot 5 \cdot 7^{8} \cdot 11 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$1$	$1$		$3$	$960$	$0.859416$	$4733169839/231139696095$	$[1, 0, 0, 35, -23128]$	\(y^2+xy=x^3+35x-23128\)
1155.g1	1155d1	1155.g	1155d	$1$	$1$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{5} \cdot 5 \cdot 7 \cdot 11^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.286254962$	$1$		$6$	$400$	$0.437218$	$-250523582464/1369738755$	$[0, -1, 1, -131, 1916]$	\(y^2+y=x^3-x^2-131x+1916\)
1155.h1	1155j2	1155.h	1155j	$2$	$3$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3 \cdot 5^{3} \cdot 7 \cdot 11^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$5.610642804$	$1$		$0$	$432$	$0.323350$	$-65860951343104/3493875$	$[0, 1, 1, -841, -9674]$	\(y^2+y=x^3+x^2-841x-9674\)
1155.h2	1155j1	1155.h	1155j	$2$	$3$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{3} \cdot 5 \cdot 7^{3} \cdot 11 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$1.870214268$	$1$		$6$	$144$	$-0.225955$	$-262144/509355$	$[0, 1, 1, -1, -35]$	\(y^2+y=x^3+x^2-x-35\)
1155.i1	1155k1	1155.i	1155k	$1$	$1$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{7} \cdot 5^{7} \cdot 7 \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$0.066101914$	$1$		$10$	$784$	$0.629956$	$17869652393984/13156171875$	$[0, 1, 1, 545, 2734]$	\(y^2+y=x^3+x^2+545x+2734\)
1155.j1	1155c3	1155.j	1155c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3 \cdot 5^{3} \cdot 7^{4} \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1$	$1$		$0$	$1152$	$0.751596$	$1058993490188089/13182390375$	$[1, 1, 0, -2123, -38142]$	\(y^2+xy=x^3+x^2-2123x-38142\)
1155.j2	1155c2	1155.j	1155c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{2} \cdot 5^{6} \cdot 7^{2} \cdot 11^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$576$	$0.405023$	$1697509118089/833765625$	$[1, 1, 0, -248, 483]$	\(y^2+xy=x^3+x^2-248x+483\)
1155.j3	1155c1	1155.j	1155c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1$	$1$		$1$	$288$	$0.058449$	$932288503609/779625$	$[1, 1, 0, -203, 1032]$	\(y^2+xy=x^3+x^2-203x+1032\)
1155.j4	1155c4	1155.j	1155c	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3 \cdot 5^{12} \cdot 7 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1$	$4$	$2$	$0$	$1152$	$0.751596$	$82375335041831/56396484375$	$[1, 1, 0, 907, 4872]$	\(y^2+xy=x^3+x^2+907x+4872\)
1155.k1	1155f3	1155.k	1155f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5^{12} \cdot 7^{4} \cdot 11 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$1.118052497$	$1$		$6$	$4608$	$1.515476$	$981281029968144361/522287841796875$	$[1, 1, 0, -20702, -333459]$	\(y^2+xy=x^3+x^2-20702x-333459\)
1155.k2	1155f2	1155.k	1155f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{8} \cdot 5^{6} \cdot 7^{2} \cdot 11^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$2.236104994$	$1$		$6$	$2304$	$1.168903$	$474334834335054841/607815140625$	$[1, 1, 0, -16247, -803016]$	\(y^2+xy=x^3+x^2-16247x-803016\)
1155.k3	1155f1	1155.k	1155f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5^{3} \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$4.472209988$	$1$		$3$	$1152$	$0.822330$	$473897054735271721/779625$	$[1, 1, 0, -16242, -803529]$	\(y^2+xy=x^3+x^2-16242x-803529\)
1155.k4	1155f4	1155.k	1155f	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{16} \cdot 5^{3} \cdot 7 \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$4.472209988$	$1$		$0$	$4608$	$1.515476$	$-185077034913624841/551466161890875$	$[1, 1, 0, -11872, -1239641]$	\(y^2+xy=x^3+x^2-11872x-1239641\)
1155.l1	1155h3	1155.l	1155h	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5 \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$4.682086988$	$1$		$0$	$384$	$0.363592$	$957681397954009/31185$	$[1, 0, 1, -2054, -35989]$	\(y^2+xy+y=x^3-2054x-35989\)
1155.l2	1155h4	1155.l	1155h	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3 \cdot 5 \cdot 7^{4} \cdot 11^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$1.170521747$	$1$		$2$	$384$	$0.363592$	$932288503609/527295615$	$[1, 0, 1, -204, 151]$	\(y^2+xy+y=x^3-204x+151\)
1155.l3	1155h2	1155.l	1155h	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$2.341043494$	$1$		$4$	$192$	$0.017018$	$234770924809/1334025$	$[1, 0, 1, -129, -569]$	\(y^2+xy+y=x^3-129x-569\)
1155.l4	1155h1	1155.l	1155h	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3 \cdot 5^{4} \cdot 7 \cdot 11 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$4.682086988$	$1$		$1$	$96$	$-0.329555$	$-4826809/144375$	$[1, 0, 1, -4, -19]$	\(y^2+xy+y=x^3-4x-19\)
1155.m1	1155l3	1155.m	1155l	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{4} \cdot 5^{4} \cdot 7^{4} \cdot 11^{3} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$1$	$1$		$2$	$7680$	$1.743290$	$21026497979043461623321/161783881875$	$[1, 0, 1, -575018, 167782133]$	\(y^2+xy+y=x^3-575018x+167782133\)
1155.m2	1155l2	1155.m	1155l	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{8} \cdot 5^{2} \cdot 7^{2} \cdot 11^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$3840$	$1.396715$	$5143681768032498601/14238434358225$	$[1, 0, 1, -35963, 2615681]$	\(y^2+xy+y=x^3-35963x+2615681\)
1155.m3	1155l4	1155.m	1155l	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{4} \cdot 5 \cdot 7 \cdot 11^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$1$	$4$	$2$	$0$	$7680$	$1.743290$	$-1143792273008057401/8897444448004035$	$[1, 0, 1, -21788, 4702241]$	\(y^2+xy+y=x^3-21788x+4702241\)
1155.m4	1155l1	1155.m	1155l	$4$	$4$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( 3^{16} \cdot 5 \cdot 7 \cdot 11^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$1$	$1$		$1$	$1920$	$1.050142$	$3481467828171481/2005331497785$	$[1, 0, 1, -3158, 4403]$	\(y^2+xy+y=x^3-3158x+4403\)
1155.n1	1155b1	1155.n	1155b	$1$	$1$	\( 3 \cdot 5 \cdot 7 \cdot 11 \)	\( - 3^{13} \cdot 5 \cdot 7^{7} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$9.244433869$	$1$		$0$	$4368$	$1.345606$	$63090423356788736/72214645051395$	$[0, -1, 1, 8294, 284721]$	\(y^2+y=x^3-x^2+8294x+284721\)