Elliptic curve search results

Results (32 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	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
1666.d1	1666a1	1666.d	1666a	$1$	$1$	\( 2 \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$0.441794610$	$1$		$6$	$672$	$0.361417$	$-208537/68$	$0.77633$	$3.80984$	$[1, 1, 0, -221, -1679]$	\(y^2+xy=x^3+x^2-221x-1679\)	68.2.0.a.1	$[(20, 39)]$
1666.f1	1666e1	1666.f	1666e	$1$	$1$	\( 2 \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$0.313271241$	$1$		$4$	$96$	$-0.611538$	$-208537/68$	$0.77633$	$2.23594$	$[1, 0, 1, -5, 4]$	\(y^2+xy+y=x^3-5x+4\)	68.2.0.a.1	$[(1, 0)]$
13328.j1	13328t1	13328.j	13328t	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 17 \)	\( - 2^{14} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$2304$	$0.081609$	$-208537/68$	$0.77633$	$2.62217$	$[0, -1, 0, -72, -272]$	\(y^2=x^3-x^2-72x-272\)	68.2.0.a.1	$[]$
13328.r1	13328h1	13328.r	13328h	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 17 \)	\( - 2^{14} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$16128$	$1.054565$	$-208537/68$	$0.77633$	$3.85147$	$[0, 1, 0, -3544, 100372]$	\(y^2=x^3+x^2-3544x+100372\)	68.2.0.a.1	$[]$
14994.br1	14994cl1	14994.br	14994cl	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 3^{6} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$2880$	$-0.062232$	$-208537/68$	$0.77633$	$2.41054$	$[1, -1, 1, -41, -115]$	\(y^2+xy+y=x^3-x^2-41x-115\)	68.2.0.a.1	$[]$
14994.cs1	14994ca1	14994.cs	14994ca	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 3^{6} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$20160$	$0.910724$	$-208537/68$	$0.77633$	$3.62478$	$[1, -1, 1, -1994, 43341]$	\(y^2+xy+y=x^3-x^2-1994x+43341\)	68.2.0.a.1	$[]$
28322.f1	28322e1	28322.f	28322e	$1$	$1$	\( 2 \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{2} \cdot 7^{2} \cdot 17^{7} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$0.548550196$	$1$		$12$	$27648$	$0.805069$	$-208537/68$	$0.77633$	$3.27623$	$[1, 1, 0, -1306, 22184]$	\(y^2+xy=x^3+x^2-1306x+22184\)	68.2.0.a.1	$[(35, 127), (290, 4768)]$
28322.h1	28322a1	28322.h	28322a	$1$	$1$	\( 2 \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{2} \cdot 7^{8} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$10.02420864$	$1$		$0$	$193536$	$1.778025$	$-208537/68$	$0.77633$	$4.41514$	$[1, 0, 1, -64020, -7801146]$	\(y^2+xy+y=x^3-64020x-7801146\)	68.2.0.a.1	$[(24399/7, 3055149/7)]$
41650.bt1	41650bt1	41650.bt	41650bt	$1$	$1$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 5^{6} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$0.914915904$	$1$		$2$	$12288$	$0.193181$	$-208537/68$	$0.77633$	$2.46715$	$[1, 1, 1, -113, 531]$	\(y^2+xy+y=x^3+x^2-113x+531\)	68.2.0.a.1	$[(15, 42)]$
41650.cd1	41650bh1	41650.cd	41650bh	$1$	$1$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 5^{6} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$9.167111022$	$1$		$0$	$86016$	$1.166136$	$-208537/68$	$0.77633$	$3.56477$	$[1, 0, 0, -5538, -198808]$	\(y^2+xy=x^3-5538x-198808\)	68.2.0.a.1	$[(51412/19, 8981136/19)]$
53312.u1	53312v1	53312.u	53312v	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$0.739577880$	$1$		$4$	$18432$	$0.428183$	$-208537/68$	$0.77633$	$2.67029$	$[0, -1, 0, -289, 2465]$	\(y^2=x^3-x^2-289x+2465\)	68.2.0.a.1	$[(-7, 64)]$
53312.x1	53312bj1	53312.x	53312bj	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$129024$	$1.401138$	$-208537/68$	$0.77633$	$3.74302$	$[0, -1, 0, -14177, 817153]$	\(y^2=x^3-x^2-14177x+817153\)	68.2.0.a.1	$[]$
53312.bq1	53312bz1	53312.bq	53312bz	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$18432$	$0.428183$	$-208537/68$	$0.77633$	$2.67029$	$[0, 1, 0, -289, -2465]$	\(y^2=x^3+x^2-289x-2465\)	68.2.0.a.1	$[]$
53312.bt1	53312b1	53312.bt	53312b	$1$	$1$	\( 2^{6} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$2.952893208$	$1$		$0$	$129024$	$1.401138$	$-208537/68$	$0.77633$	$3.74302$	$[0, 1, 0, -14177, -817153]$	\(y^2=x^3+x^2-14177x-817153\)	68.2.0.a.1	$[(2251/3, 90944/3)]$
119952.bo1	119952fe1	119952.bo	119952fe	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{14} \cdot 3^{6} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$69120$	$0.630916$	$-208537/68$	$0.77633$	$2.69316$	$[0, 0, 0, -651, 7994]$	\(y^2=x^3-651x+7994\)	68.2.0.a.1	$[]$
119952.fn1	119952ea1	119952.fn	119952ea	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{14} \cdot 3^{6} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$9$	$3$	$0$	$483840$	$1.603870$	$-208537/68$	$0.77633$	$3.69150$	$[0, 0, 0, -31899, -2741942]$	\(y^2=x^3-31899x-2741942\)	68.2.0.a.1	$[]$
201586.cf1	201586n1	201586.cf	201586n	$1$	$1$	\( 2 \cdot 7^{2} \cdot 11^{2} \cdot 17 \)	\( - 2^{2} \cdot 7^{8} \cdot 11^{6} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$960960$	$1.560366$	$-208537/68$	$0.77633$	$3.49186$	$[1, 1, 1, -26804, 2100825]$	\(y^2+xy+y=x^3+x^2-26804x+2100825\)	68.2.0.a.1	$[]$
201586.dg1	201586bo1	201586.dg	201586bo	$1$	$1$	\( 2 \cdot 7^{2} \cdot 11^{2} \cdot 17 \)	\( - 2^{2} \cdot 7^{2} \cdot 11^{6} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$9$	$3$	$0$	$137280$	$0.587410$	$-208537/68$	$0.77633$	$2.53595$	$[1, 0, 0, -547, -6203]$	\(y^2+xy=x^3-547x-6203\)	68.2.0.a.1	$[]$
226576.bj1	226576x1	226576.bj	226576x	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{14} \cdot 7^{8} \cdot 17^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$4644864$	$2.471172$	$-208537/68$	$0.77633$	$4.34513$	$[0, -1, 0, -1024312, 499273328]$	\(y^2=x^3-x^2-1024312x+499273328\)	68.2.0.a.1	$[]$
226576.cf1	226576bn1	226576.cf	226576bn	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{14} \cdot 7^{2} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$3.572699573$	$1$		$0$	$663552$	$1.498217$	$-208537/68$	$0.77633$	$3.39828$	$[0, 1, 0, -20904, -1461580]$	\(y^2=x^3+x^2-20904x-1461580\)	68.2.0.a.1	$[(877/2, 17051/2)]$
254898.fe1	254898fe1	254898.fe	254898fe	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{2} \cdot 3^{6} \cdot 7^{8} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$6.192178821$	$1$		$0$	$5806080$	$2.327332$	$-208537/68$	$0.77633$	$4.16536$	$[1, -1, 1, -576176, 210630935]$	\(y^2+xy+y=x^3-x^2-576176x+210630935\)	68.2.0.a.1	$[(-5147/4, 1228975/4)]$
254898.hi1	254898hi1	254898.hi	254898hi	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{2} \cdot 3^{6} \cdot 7^{2} \cdot 17^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$829440$	$1.354376$	$-208537/68$	$0.77633$	$3.22747$	$[1, -1, 1, -11759, -610725]$	\(y^2+xy+y=x^3-x^2-11759x-610725\)	68.2.0.a.1	$[]$
281554.cz1	281554cz1	281554.cz	281554cz	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	\( - 2^{2} \cdot 7^{8} \cdot 13^{6} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$1378944$	$1.643892$	$-208537/68$	$0.77633$	$3.47876$	$[1, 1, 1, -37437, -3501737]$	\(y^2+xy+y=x^3+x^2-37437x-3501737\)	68.2.0.a.1	$[]$
281554.dj1	281554dj1	281554.dj	281554dj	$1$	$1$	\( 2 \cdot 7^{2} \cdot 13^{2} \cdot 17 \)	\( - 2^{2} \cdot 7^{2} \cdot 13^{6} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$196992$	$0.670937$	$-208537/68$	$0.77633$	$2.54830$	$[1, 0, 0, -764, 10100]$	\(y^2+xy=x^3-764x+10100\)	68.2.0.a.1	$[]$
333200.ce1	333200ce1	333200.ce	333200ce	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{14} \cdot 5^{6} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$0.796345606$	$1$		$6$	$2064384$	$1.859283$	$-208537/68$	$0.77633$	$3.63594$	$[0, -1, 0, -88608, 12723712]$	\(y^2=x^3-x^2-88608x+12723712\)	68.2.0.a.1	$[(82, 2450)]$
333200.fk1	333200fk1	333200.fk	333200fk	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{14} \cdot 5^{6} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$6.994956287$	$1$		$0$	$294912$	$0.886329$	$-208537/68$	$0.77633$	$2.71781$	$[0, 1, 0, -1808, -37612]$	\(y^2=x^3+x^2-1808x-37612\)	68.2.0.a.1	$[(7748/11, 447950/11)]$
374850.el1	374850el1	374850.el	374850el	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 3^{6} \cdot 5^{6} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$2580480$	$1.715443$	$-208537/68$	$0.77633$	$3.46808$	$[1, -1, 0, -49842, 5367816]$	\(y^2+xy=x^3-x^2-49842x+5367816\)	68.2.0.a.1	$[]$
374850.ev1	374850ev1	374850.ev	374850ev	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{2} \cdot 3^{6} \cdot 5^{6} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$368640$	$0.742488$	$-208537/68$	$0.77633$	$2.55837$	$[1, -1, 0, -1017, -15359]$	\(y^2+xy=x^3-x^2-1017x-15359\)	68.2.0.a.1	$[]$
479808.ds1	479808ds1	479808.ds	479808ds	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 3^{6} \cdot 7^{8} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$0.901939513$	$1$		$4$	$3870720$	$1.950445$	$-208537/68$	$0.77633$	$3.61822$	$[0, 0, 0, -127596, 21935536]$	\(y^2=x^3-127596x+21935536\)	68.2.0.a.1	$[(294, 3136)]$
479808.ej1	479808ej1	479808.ej	479808ej	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 3^{6} \cdot 7^{8} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$3870720$	$1.950445$	$-208537/68$	$0.77633$	$3.61822$	$[0, 0, 0, -127596, -21935536]$	\(y^2=x^3-127596x-21935536\)	68.2.0.a.1	$[]$
479808.nw1	479808nw1	479808.nw	479808nw	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 3^{6} \cdot 7^{2} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$8.590979876$	$1$		$0$	$552960$	$0.977489$	$-208537/68$	$0.77633$	$2.72567$	$[0, 0, 0, -2604, -63952]$	\(y^2=x^3-2604x-63952\)	68.2.0.a.1	$[(60134/5, 14742848/5)]$
479808.ol1	479808ol1	479808.ol	479808ol	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{20} \cdot 3^{6} \cdot 7^{2} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$68$	$2$	$0$	$1$	$1$		$0$	$552960$	$0.977489$	$-208537/68$	$0.77633$	$2.72567$	$[0, 0, 0, -2604, 63952]$	\(y^2=x^3-2604x+63952\)	68.2.0.a.1	$[]$