Elliptic curve search results

Results (28 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
1950.e1	1950c1	1950.e	1950c	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2 \cdot 3 \cdot 5^{8} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$840$	$0.120104$	$34295/78$	$0.80517$	$3.21999$	$[1, 1, 0, 50, 250]$	\(y^2+xy=x^3+x^2+50x+250\)	312.2.0.?	$[]$
1950.x1	1950z1	1950.x	1950z	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2 \cdot 3 \cdot 5^{2} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$168$	$-0.684615$	$34295/78$	$0.80517$	$1.94529$	$[1, 0, 0, 2, 2]$	\(y^2+xy=x^3+2x+2\)	312.2.0.?	$[]$
5850.a1	5850s1	5850.a	5850s	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2 \cdot 3^{7} \cdot 5^{2} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$0.438678381$	$1$		$4$	$1344$	$-0.135309$	$34295/78$	$0.80517$	$2.45883$	$[1, -1, 0, 18, -54]$	\(y^2+xy=x^3-x^2+18x-54\)	312.2.0.?	$[(3, 3)]$
5850.by1	5850bx1	5850.by	5850bx	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2 \cdot 3^{7} \cdot 5^{8} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$6720$	$0.669411$	$34295/78$	$0.80517$	$3.57209$	$[1, -1, 1, 445, -6303]$	\(y^2+xy+y=x^3-x^2+445x-6303\)	312.2.0.?	$[]$
15600.bg1	15600bn1	15600.bg	15600bn	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{13} \cdot 3 \cdot 5^{2} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$0.895351912$	$1$		$2$	$4032$	$0.008532$	$34295/78$	$0.80517$	$2.38782$	$[0, -1, 0, 32, -128]$	\(y^2=x^3-x^2+32x-128\)	312.2.0.?	$[(8, 24)]$
15600.bo1	15600cq1	15600.bo	15600cq	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{13} \cdot 3 \cdot 5^{8} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$20160$	$0.813251$	$34295/78$	$0.80517$	$3.38798$	$[0, 1, 0, 792, -14412]$	\(y^2=x^3+x^2+792x-14412\)	312.2.0.?	$[]$
25350.bs1	25350bh1	25350.bs	25350bh	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2 \cdot 3 \cdot 5^{2} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$28224$	$0.597860$	$34295/78$	$0.80517$	$2.97089$	$[1, 0, 1, 334, 4058]$	\(y^2+xy+y=x^3+334x+4058\)	312.2.0.?	$[]$
25350.bx1	25350cj1	25350.bx	25350cj	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2 \cdot 3 \cdot 5^{8} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1.065702979$	$1$		$0$	$141120$	$1.402578$	$34295/78$	$0.80517$	$3.92317$	$[1, 1, 1, 8362, 507281]$	\(y^2+xy+y=x^3+x^2+8362x+507281\)	312.2.0.?	$[(215/2, 8231/2)]$
46800.r1	46800fa1	46800.r	46800fa	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{13} \cdot 3^{7} \cdot 5^{8} \cdot 13 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$0.439999051$	$1$		$22$	$161280$	$1.362558$	$34295/78$	$0.80517$	$3.65483$	$[0, 0, 0, 7125, 396250]$	\(y^2=x^3+7125x+396250\)	312.2.0.?	$[(125, 1800), (29, 792)]$
46800.fo1	46800ei1	46800.fo	46800ei	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{13} \cdot 3^{7} \cdot 5^{2} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$32256$	$0.557838$	$34295/78$	$0.80517$	$2.75685$	$[0, 0, 0, 285, 3170]$	\(y^2=x^3+285x+3170\)	312.2.0.?	$[]$
62400.e1	62400t1	62400.e	62400t	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3 \cdot 5^{2} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$0.533666037$	$1$		$6$	$32256$	$0.355106$	$34295/78$	$0.80517$	$2.46468$	$[0, -1, 0, 127, 897]$	\(y^2=x^3-x^2+127x+897\)	312.2.0.?	$[(1, 32)]$
62400.s1	62400fz1	62400.s	62400fz	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3 \cdot 5^{8} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$161280$	$1.159824$	$34295/78$	$0.80517$	$3.33927$	$[0, -1, 0, 3167, -118463]$	\(y^2=x^3-x^2+3167x-118463\)	312.2.0.?	$[]$
62400.hp1	62400du1	62400.hp	62400du	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3 \cdot 5^{8} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$161280$	$1.159824$	$34295/78$	$0.80517$	$3.33927$	$[0, 1, 0, 3167, 118463]$	\(y^2=x^3+x^2+3167x+118463\)	312.2.0.?	$[]$
62400.ic1	62400gs1	62400.ic	62400gs	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3 \cdot 5^{2} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$2.856768650$	$1$		$2$	$32256$	$0.355106$	$34295/78$	$0.80517$	$2.46468$	$[0, 1, 0, 127, -897]$	\(y^2=x^3+x^2+127x-897\)	312.2.0.?	$[(159, 2016)]$
76050.l1	76050cv1	76050.l	76050cv	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( - 2 \cdot 3^{7} \cdot 5^{8} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$2.497131338$	$1$		$2$	$1128960$	$1.951885$	$34295/78$	$0.80517$	$4.12617$	$[1, -1, 0, 75258, -13621334]$	\(y^2+xy=x^3-x^2+75258x-13621334\)	312.2.0.?	$[(725, 20171)]$
76050.ge1	76050ex1	76050.ge	76050ex	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( - 2 \cdot 3^{7} \cdot 5^{2} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$4.105148166$	$1$		$0$	$225792$	$1.147165$	$34295/78$	$0.80517$	$3.26698$	$[1, -1, 1, 3010, -109573]$	\(y^2+xy+y=x^3-x^2+3010x-109573\)	312.2.0.?	$[(2565/4, 130207/4)]$
95550.fn1	95550ft1	95550.fn	95550ft	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2 \cdot 3 \cdot 5^{8} \cdot 7^{6} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$2.469133503$	$1$		$0$	$241920$	$1.093060$	$34295/78$	$0.80517$	$3.14533$	$[1, 0, 1, 2424, -78452]$	\(y^2+xy+y=x^3+2424x-78452\)	312.2.0.?	$[(583/2, 14113/2)]$
95550.ig1	95550gu1	95550.ig	95550gu	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2 \cdot 3 \cdot 5^{2} \cdot 7^{6} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$5.385081087$	$1$		$0$	$48384$	$0.288340$	$34295/78$	$0.80517$	$2.30324$	$[1, 1, 1, 97, -589]$	\(y^2+xy+y=x^3+x^2+97x-589\)	312.2.0.?	$[(719/10, 19327/10)]$
187200.p1	187200d1	187200.p	187200d	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{8} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$2.074099562$	$1$		$4$	$1290240$	$1.709131$	$34295/78$	$0.80517$	$3.58006$	$[0, 0, 0, 28500, 3170000]$	\(y^2=x^3+28500x+3170000\)	312.2.0.?	$[(-86, 288)]$
187200.br1	187200kx1	187200.br	187200kx	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{2} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$258048$	$0.904412$	$34295/78$	$0.80517$	$2.78461$	$[0, 0, 0, 1140, -25360]$	\(y^2=x^3+1140x-25360\)	312.2.0.?	$[]$
187200.ox1	187200gb1	187200.ox	187200gb	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{2} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1.787049259$	$1$		$2$	$258048$	$0.904412$	$34295/78$	$0.80517$	$2.78461$	$[0, 0, 0, 1140, 25360]$	\(y^2=x^3+1140x+25360\)	312.2.0.?	$[(-4, 144)]$
187200.pz1	187200km1	187200.pz	187200km	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{19} \cdot 3^{7} \cdot 5^{8} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$1290240$	$1.709131$	$34295/78$	$0.80517$	$3.58006$	$[0, 0, 0, 28500, -3170000]$	\(y^2=x^3+28500x-3170000\)	312.2.0.?	$[]$
202800.o1	202800eq1	202800.o	202800eq	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{13} \cdot 3 \cdot 5^{2} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$677376$	$1.291008$	$34295/78$	$0.80517$	$3.14601$	$[0, -1, 0, 5352, -259728]$	\(y^2=x^3-x^2+5352x-259728\)	312.2.0.?	$[]$
202800.ke1	202800bj1	202800.ke	202800bj	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{13} \cdot 3 \cdot 5^{8} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$3386880$	$2.095726$	$34295/78$	$0.80517$	$3.93624$	$[0, 1, 0, 133792, -32198412]$	\(y^2=x^3+x^2+133792x-32198412\)	312.2.0.?	$[]$
235950.eh1	235950eh1	235950.eh	235950eh	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( - 2 \cdot 3 \cdot 5^{2} \cdot 11^{6} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$6.310071736$	$1$		$0$	$215040$	$0.514333$	$34295/78$	$0.80517$	$2.35415$	$[1, 0, 1, 239, -2422]$	\(y^2+xy+y=x^3+239x-2422\)	312.2.0.?	$[(4242/13, 278608/13)]$
235950.er1	235950er1	235950.er	235950er	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \cdot 13 \)	\( - 2 \cdot 3 \cdot 5^{8} \cdot 11^{6} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$8.111821654$	$1$		$0$	$1075200$	$1.319052$	$34295/78$	$0.80517$	$3.13471$	$[1, 1, 1, 5987, -302719]$	\(y^2+xy+y=x^3+x^2+5987x-302719\)	312.2.0.?	$[(35989/4, 6761223/4)]$
286650.w1	286650w1	286650.w	286650w	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2 \cdot 3^{7} \cdot 5^{2} \cdot 7^{6} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$0.920538267$	$1$		$4$	$387072$	$0.837646$	$34295/78$	$0.80517$	$2.62643$	$[1, -1, 0, 873, 16771]$	\(y^2+xy=x^3-x^2+873x+16771\)	312.2.0.?	$[(23, 209)]$
286650.kd1	286650kd1	286650.kd	286650kd	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 13 \)	\( - 2 \cdot 3^{7} \cdot 5^{8} \cdot 7^{6} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$312$	$2$	$0$	$1$	$1$		$0$	$1935360$	$1.642365$	$34295/78$	$0.80517$	$3.39491$	$[1, -1, 1, 21820, 2118197]$	\(y^2+xy+y=x^3-x^2+21820x+2118197\)	312.2.0.?	$[]$