Elliptic curve search results

Results (30 matches)

  Download displayed columns for results to

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
2856.i2	2856a1	2856.i	2856a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$16896$	$1.592707$	$-23707171994692/1480419781911$	$1.02023$	$5.33088$	$[0, 1, 0, -6032, 1879920]$	\(y^2=x^3+x^2-6032x+1879920\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
5712.l2	5712d1	5712.l	5712d	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$4$	$2$	$1$	$33792$	$1.592707$	$-23707171994692/1480419781911$	$1.02023$	$4.90372$	$[0, -1, 0, -6032, -1879920]$	\(y^2=x^3-x^2-6032x-1879920\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
8568.b2	8568j1	8568.b	8568j	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{22} \cdot 7 \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$135168$	$2.142014$	$-23707171994692/1480419781911$	$1.02023$	$5.41206$	$[0, 0, 0, -54291, -50812130]$	\(y^2=x^3-54291x-50812130\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
17136.n2	17136l1	17136.n	17136l	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{22} \cdot 7 \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$270336$	$2.142014$	$-23707171994692/1480419781911$	$1.02023$	$5.02726$	$[0, 0, 0, -54291, 50812130]$	\(y^2=x^3-54291x+50812130\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
19992.g2	19992j1	19992.g	19992j	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 7^{7} \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$8.130082885$	$1$		$3$	$811008$	$2.565662$	$-23707171994692/1480419781911$	$1.02023$	$5.46236$	$[0, -1, 0, -295584, -645403716]$	\(y^2=x^3-x^2-295584x-645403716\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(62930, 15785792)]$
22848.d2	22848c1	22848.d	22848c	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 17 \)	\( - 2^{16} \cdot 3^{16} \cdot 7 \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$4.312862518$	$1$		$3$	$270336$	$1.939281$	$-23707171994692/1480419781911$	$1.02023$	$4.64077$	$[0, -1, 0, -24129, 15063489]$	\(y^2=x^3-x^2-24129x+15063489\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(-151, 3904)]$
22848.bz2	22848ct1	22848.bz	22848ct	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 17 \)	\( - 2^{16} \cdot 3^{16} \cdot 7 \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$270336$	$1.939281$	$-23707171994692/1480419781911$	$1.02023$	$4.64077$	$[0, 1, 0, -24129, -15063489]$	\(y^2=x^3+x^2-24129x-15063489\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
39984.cg2	39984z1	39984.cg	39984z	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 7^{7} \cdot 17^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$0.321895478$	$1$		$41$	$1622016$	$2.565662$	$-23707171994692/1480419781911$	$1.02023$	$5.10504$	$[0, 1, 0, -295584, 645403716]$	\(y^2=x^3+x^2-295584x+645403716\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(480, 24786), (5070, 359856)]$
48552.e2	48552k1	48552.e	48552k	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 17^{2} \)	\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 17^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$4866048$	$3.009315$	$-23707171994692/1480419781911$	$1.02023$	$5.50657$	$[0, -1, 0, -1743344, 9246506844]$	\(y^2=x^3-x^2-1743344x+9246506844\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
59976.bf2	59976bi1	59976.bf	59976bi	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{22} \cdot 7^{7} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$6488064$	$3.114967$	$-23707171994692/1480419781911$	$1.02023$	$5.51605$	$[0, 0, 0, -2660259, 17428560590]$	\(y^2=x^3-2660259x+17428560590\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
68544.dx2	68544bo1	68544.dx	68544bo	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{16} \cdot 3^{22} \cdot 7 \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$7.183600562$	$1$		$1$	$2162688$	$2.488586$	$-23707171994692/1480419781911$	$1.02023$	$4.77487$	$[0, 0, 0, -217164, -406497040]$	\(y^2=x^3-217164x-406497040\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(36326/5, 6054176/5)]$
68544.dy2	68544eu1	68544.dy	68544eu	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 17 \)	\( - 2^{16} \cdot 3^{22} \cdot 7 \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$3.600829837$	$1$		$5$	$2162688$	$2.488586$	$-23707171994692/1480419781911$	$1.02023$	$4.77487$	$[0, 0, 0, -217164, 406497040]$	\(y^2=x^3-217164x+406497040\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(-822, 5440)]$
71400.cg2	71400cz1	71400.cg	71400cz	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 5^{6} \cdot 7 \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$2162688$	$2.397427$	$-23707171994692/1480419781911$	$1.02023$	$4.65955$	$[0, -1, 0, -150808, 235291612]$	\(y^2=x^3-x^2-150808x+235291612\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
97104.by2	97104u1	97104.by	97104u	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 17^{2} \)	\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 17^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$9732096$	$3.009315$	$-23707171994692/1480419781911$	$1.02023$	$5.17419$	$[0, 1, 0, -1743344, -9246506844]$	\(y^2=x^3+x^2-1743344x-9246506844\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
119952.fy2	119952z1	119952.fy	119952z	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{22} \cdot 7^{7} \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$12.97690779$	$1$		$1$	$12976128$	$3.114967$	$-23707171994692/1480419781911$	$1.02023$	$5.18911$	$[0, 0, 0, -2660259, -17428560590]$	\(y^2=x^3-2660259x-17428560590\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(10750418/47, 30249332190/47)]$
142800.eu2	142800gr1	142800.eu	142800gr	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 5^{6} \cdot 7 \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$0.379279132$	$1$		$13$	$4325376$	$2.397427$	$-23707171994692/1480419781911$	$1.02023$	$4.38744$	$[0, 1, 0, -150808, -235291612]$	\(y^2=x^3+x^2-150808x-235291612\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(968, 22950)]$
145656.bl2	145656s1	145656.bl	145656s	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 17^{2} \)	\( - 2^{10} \cdot 3^{22} \cdot 7 \cdot 17^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$49$	$7$	$1$	$38928384$	$3.558620$	$-23707171994692/1480419781911$	$1.02023$	$5.55217$	$[0, 0, 0, -15690099, -249639994690]$	\(y^2=x^3-15690099x-249639994690\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
159936.em2	159936es1	159936.em	159936es	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( - 2^{16} \cdot 3^{16} \cdot 7^{7} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$12976128$	$2.912235$	$-23707171994692/1480419781911$	$1.02023$	$4.86150$	$[0, -1, 0, -1182337, 5164412065]$	\(y^2=x^3-x^2-1182337x+5164412065\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
159936.je2	159936hc1	159936.je	159936hc	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 17 \)	\( - 2^{16} \cdot 3^{16} \cdot 7^{7} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$12976128$	$2.912235$	$-23707171994692/1480419781911$	$1.02023$	$4.86150$	$[0, 1, 0, -1182337, -5164412065]$	\(y^2=x^3+x^2-1182337x-5164412065\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
214200.ch2	214200di1	214200.ch	214200di	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{22} \cdot 5^{6} \cdot 7 \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$13.98644269$	$1$		$1$	$17301504$	$2.946732$	$-23707171994692/1480419781911$	$1.02023$	$4.77952$	$[0, 0, 0, -1357275, -6351516250]$	\(y^2=x^3-1357275x-6351516250\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(12964030/61, 40099290750/61)]$
291312.eh2	291312eh1	291312.eh	291312eh	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 17^{2} \)	\( - 2^{10} \cdot 3^{22} \cdot 7 \cdot 17^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$77856768$	$3.558620$	$-23707171994692/1480419781911$	$1.02023$	$5.24630$	$[0, 0, 0, -15690099, 249639994690]$	\(y^2=x^3-15690099x+249639994690\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
339864.cq2	339864cq1	339864.cq	339864cq	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 17^{2} \)	\( - 2^{10} \cdot 3^{16} \cdot 7^{7} \cdot 17^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$6.490989944$	$1$		$3$	$233570304$	$3.982269$	$-23707171994692/1480419781911$	$1.02023$	$5.58196$	$[0, 1, 0, -85423872, -3171380999760]$	\(y^2=x^3+x^2-85423872x-3171380999760\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(66669/2, 1501605/2)]$
345576.bw2	345576bw1	345576.bw	345576bw	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 11^{6} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$18247680$	$2.791656$	$-23707171994692/1480419781911$	$1.02023$	$4.45435$	$[0, 1, 0, -729912, -2505093120]$	\(y^2=x^3+x^2-729912x-2505093120\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
388416.da2	388416da1	388416.da	388416da	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} \)	\( - 2^{16} \cdot 3^{16} \cdot 7 \cdot 17^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$77856768$	$3.355888$	$-23707171994692/1480419781911$	$1.02023$	$4.94000$	$[0, -1, 0, -6973377, -73965081375]$	\(y^2=x^3-x^2-6973377x-73965081375\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
388416.hw2	388416hw1	388416.hw	388416hw	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 17^{2} \)	\( - 2^{16} \cdot 3^{16} \cdot 7 \cdot 17^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$3.278545686$	$1$		$1$	$77856768$	$3.355888$	$-23707171994692/1480419781911$	$1.02023$	$4.94000$	$[0, 1, 0, -6973377, 73965081375]$	\(y^2=x^3+x^2-6973377x+73965081375\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(-26151/7, 95508720/7)]$
428400.hg2	428400hg1	428400.hg	428400hg	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 17 \)	\( - 2^{10} \cdot 3^{22} \cdot 5^{6} \cdot 7 \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$34603008$	$2.946732$	$-23707171994692/1480419781911$	$1.02023$	$4.52405$	$[0, 0, 0, -1357275, 6351516250]$	\(y^2=x^3-1357275x+6351516250\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
479808.da2	479808da1	479808.da	479808da	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{16} \cdot 3^{22} \cdot 7^{7} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$103809024$	$3.461540$	$-23707171994692/1480419781911$	$1.02023$	$4.95712$	$[0, 0, 0, -10641036, -139428484720]$	\(y^2=x^3-10641036x-139428484720\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
479808.fe2	479808fe1	479808.fe	479808fe	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{16} \cdot 3^{22} \cdot 7^{7} \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$18.30792011$	$1$		$1$	$103809024$	$3.461540$	$-23707171994692/1480419781911$	$1.02023$	$4.95712$	$[0, 0, 0, -10641036, 139428484720]$	\(y^2=x^3-10641036x+139428484720\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[(904653414/655, 99893955775712/655)]$
482664.bi2	482664bi1	482664.bi	482664bi	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 13^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 13^{6} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$36495360$	$2.875183$	$-23707171994692/1480419781911$	$1.02023$	$4.41722$	$[0, 1, 0, -1019464, 4134262016]$	\(y^2=x^3+x^2-1019464x+4134262016\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$
499800.jl2	499800jl1	499800.jl	499800jl	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{16} \cdot 5^{6} \cdot 7^{7} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$952$	$12$	$0$	$1$	$1$		$1$	$103809024$	$3.370380$	$-23707171994692/1480419781911$	$1.02023$	$4.85833$	$[0, 1, 0, -7389608, -80690243712]$	\(y^2=x^3+x^2-7389608x-80690243712\)	2.3.0.a.1, 8.6.0.c.1, 238.6.0.?, 952.12.0.?	$[ ]$

  Download displayed columns for results to