Elliptic curve search results

Results (12 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
12090.p3	12090j4	12090.p	12090j	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 31 \)	\( - 2^{2} \cdot 3^{12} \cdot 5 \cdot 13 \cdot 31^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$48360$	$48$	$0$	$1$	$1$		$0$	$49152$	$1.411680$	$-254850956966062729/127607200177860$	$0.94413$	$4.33003$	$[1, 0, 1, -13209, -799088]$	\(y^2+xy+y=x^3-13209x-799088\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 52.12.0-4.c.1.2, 260.24.0.?, $\ldots$	$[ ]$
36270.cc3	36270bt3	36270.cc	36270bt	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \cdot 31 \)	\( - 2^{2} \cdot 3^{18} \cdot 5 \cdot 13 \cdot 31^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$1$	$4$	$2$	$0$	$393216$	$1.960985$	$-254850956966062729/127607200177860$	$0.94413$	$4.50478$	$[1, -1, 1, -118877, 21575369]$	\(y^2+xy+y=x^3-x^2-118877x+21575369\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.1, 156.12.0.?, 248.12.0.?, $\ldots$	$[ ]$
60450.bq3	60450cc3	60450.bq	60450cc	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13 \cdot 31 \)	\( - 2^{2} \cdot 3^{12} \cdot 5^{7} \cdot 13 \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$48360$	$48$	$0$	$9.572109293$	$1$		$0$	$1179648$	$2.216400$	$-254850956966062729/127607200177860$	$0.94413$	$4.57415$	$[1, 1, 1, -330213, -99885969]$	\(y^2+xy+y=x^3+x^2-330213x-99885969\)	2.3.0.a.1, 4.12.0-4.c.1.2, 260.24.0.?, 3720.24.0.?, 9672.24.0.?, $\ldots$	$[(17119/3, 2093150/3)]$
96720.c3	96720bi3	96720.c	96720bi	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 31 \)	\( - 2^{14} \cdot 3^{12} \cdot 5 \cdot 13 \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$2.167719116$	$1$		$5$	$1179648$	$2.104828$	$-254850956966062729/127607200177860$	$0.94413$	$4.27025$	$[0, -1, 0, -211336, 51141616]$	\(y^2=x^3-x^2-211336x+51141616\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 52.12.0-4.c.1.1, 260.24.0.?, $\ldots$	$[(178, 4374)]$
157170.cy3	157170a3	157170.cy	157170a	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{2} \cdot 3^{12} \cdot 5 \cdot 13^{7} \cdot 31^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$48360$	$48$	$0$	$8.029464012$	$1$		$2$	$8257536$	$2.694153$	$-254850956966062729/127607200177860$	$0.94413$	$4.68802$	$[1, 0, 0, -2232240, -1753363548]$	\(y^2+xy=x^3-2232240x-1753363548\)	2.3.0.a.1, 4.12.0-4.c.1.1, 260.24.0.?, 3720.24.0.?, 9672.24.0.?, $\ldots$	$[(571872/17, 190347018/17)]$
181350.b3	181350dh4	181350.b	181350dh	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \cdot 31 \)	\( - 2^{2} \cdot 3^{18} \cdot 5^{7} \cdot 13 \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$3.347901863$	$1$		$4$	$9437184$	$2.765705$	$-254850956966062729/127607200177860$	$0.94413$	$4.70352$	$[1, -1, 0, -2971917, 2693949241]$	\(y^2+xy=x^3-x^2-2971917x+2693949241\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 260.12.0.?, 780.24.0.?, $\ldots$	$[(-427, 62543)]$
290160.di3	290160di3	290160.di	290160di	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \cdot 31 \)	\( - 2^{14} \cdot 3^{18} \cdot 5 \cdot 13 \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$13.24844502$	$1$		$1$	$9437184$	$2.654133$	$-254850956966062729/127607200177860$	$0.94413$	$4.42133$	$[0, 0, 0, -1902027, -1378921606]$	\(y^2=x^3-1902027x-1378921606\)	2.3.0.a.1, 4.6.0.c.1, 60.12.0-4.c.1.2, 156.12.0.?, 248.12.0.?, $\ldots$	$[(34638959/25, 203803192802/25)]$
374790.r3	374790r4	374790.r	374790r	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 31^{2} \)	\( - 2^{2} \cdot 3^{12} \cdot 5 \cdot 13 \cdot 31^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$12.97885286$	$1$		$0$	$47185920$	$3.128674$	$-254850956966062729/127607200177860$	$0.94413$	$4.77686$	$[1, 1, 0, -12693388, 23767543012]$	\(y^2+xy=x^3+x^2-12693388x+23767543012\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 260.12.0.?, 620.12.0.?, $\ldots$	$[(11641417/7, 39674885263/7)]$
386880.eg3	386880eg3	386880.eg	386880eg	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 31 \)	\( - 2^{20} \cdot 3^{12} \cdot 5 \cdot 13 \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$28.77940452$	$1$		$1$	$9437184$	$2.451401$	$-254850956966062729/127607200177860$	$0.94413$	$4.13338$	$[0, -1, 0, -845345, -408287583]$	\(y^2=x^3-x^2-845345x-408287583\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.1, 104.12.0.?, 260.12.0.?, $\ldots$	$[(6024917229319/22365, 14743090997978942528/22365)]$
386880.gx3	386880gx4	386880.gx	386880gx	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13 \cdot 31 \)	\( - 2^{20} \cdot 3^{12} \cdot 5 \cdot 13 \cdot 31^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$1$	$1$		$1$	$9437184$	$2.451401$	$-254850956966062729/127607200177860$	$0.94413$	$4.13338$	$[0, 1, 0, -845345, 408287583]$	\(y^2=x^3+x^2-845345x+408287583\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.2, 104.12.0.?, 260.12.0.?, $\ldots$	$[ ]$
471510.d3	471510d4	471510.d	471510d	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{2} \cdot 3^{18} \cdot 5 \cdot 13^{7} \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$48360$	$48$	$0$	$1.530772416$	$1$		$4$	$66060288$	$3.243462$	$-254850956966062729/127607200177860$	$0.94413$	$4.79835$	$[1, -1, 0, -20090160, 47340815796]$	\(y^2+xy=x^3-x^2-20090160x+47340815796\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 260.12.0.?, 780.24.0.?, $\ldots$	$[(2181, 116787)]$
483600.hk3	483600hk4	483600.hk	483600hk	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \cdot 31 \)	\( - 2^{14} \cdot 3^{12} \cdot 5^{7} \cdot 13 \cdot 31^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$48360$	$48$	$0$	$4.117514872$	$1$		$7$	$28311552$	$2.909546$	$-254850956966062729/127607200177860$	$0.94413$	$4.48294$	$[0, 1, 0, -5283408, 6382135188]$	\(y^2=x^3+x^2-5283408x+6382135188\)	2.3.0.a.1, 4.12.0-4.c.1.1, 260.24.0.?, 3720.24.0.?, 9672.24.0.?, $\ldots$	$[(1212, 41958)]$

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