Elliptic curve search results

Results (18 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
1006.b1	1006a1	1006.b	1006a	$1$	$1$	\( 2 \cdot 503 \)	\( - 2^{4} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1006$	$2$	$0$	$0.284628487$	$1$		$6$	$48$	$-0.569676$	$-389017/8048$	$0.80210$	$2.38301$	$[1, 0, 1, -2, 4]$	\(y^2+xy+y=x^3-2x+4\)	1006.2.0.?	$[(1, 1)]$
8048.d1	8048j1	8048.d	8048j	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{16} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.712606191$	$1$		$6$	$1152$	$0.123471$	$-389017/8048$	$0.80210$	$2.75690$	$[0, -1, 0, -24, -272]$	\(y^2=x^3-x^2-24x-272\)	1006.2.0.?	$[(12, 32)]$
9054.t1	9054s1	9054.t	9054s	$1$	$1$	\( 2 \cdot 3^{2} \cdot 503 \)	\( - 2^{4} \cdot 3^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$1440$	$-0.020371$	$-389017/8048$	$0.80210$	$2.53180$	$[1, -1, 1, -14, -115]$	\(y^2+xy+y=x^3-x^2-14x-115\)	1006.2.0.?	$[]$
25150.l1	25150o1	25150.l	25150o	$1$	$1$	\( 2 \cdot 5^{2} \cdot 503 \)	\( - 2^{4} \cdot 5^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.513807410$	$1$		$4$	$6144$	$0.235042$	$-389017/8048$	$0.80210$	$2.57901$	$[1, 1, 1, -38, 531]$	\(y^2+xy+y=x^3+x^2-38x+531\)	1006.2.0.?	$[(-5, 27)]$
32192.l1	32192c1	32192.l	32192c	$1$	$1$	\( 2^{6} \cdot 503 \)	\( - 2^{22} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1.111981705$	$1$		$2$	$9216$	$0.470044$	$-389017/8048$	$0.80210$	$2.78936$	$[0, -1, 0, -97, 2273]$	\(y^2=x^3-x^2-97x+2273\)	1006.2.0.?	$[(41, 256)]$
32192.w1	32192z1	32192.w	32192z	$1$	$1$	\( 2^{6} \cdot 503 \)	\( - 2^{22} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$3.103979421$	$1$		$0$	$9216$	$0.470044$	$-389017/8048$	$0.80210$	$2.78936$	$[0, 1, 0, -97, -2273]$	\(y^2=x^3+x^2-97x-2273\)	1006.2.0.?	$[(271/3, 4096/3)]$
49294.a1	49294b1	49294.a	49294b	$1$	$1$	\( 2 \cdot 7^{2} \cdot 503 \)	\( - 2^{4} \cdot 7^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$2.787428083$	$1$		$2$	$18144$	$0.403278$	$-389017/8048$	$0.80210$	$2.60523$	$[1, 1, 0, -74, -1532]$	\(y^2+xy=x^3+x^2-74x-1532\)	1006.2.0.?	$[(24, 94)]$
72432.bj1	72432bh1	72432.bj	72432bh	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 503 \)	\( - 2^{16} \cdot 3^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1.674305692$	$1$		$2$	$34560$	$0.672776$	$-389017/8048$	$0.80210$	$2.80463$	$[0, 0, 0, -219, 7562]$	\(y^2=x^3-219x+7562\)	1006.2.0.?	$[(29, 160)]$
121726.h1	121726g1	121726.h	121726g	$1$	$1$	\( 2 \cdot 11^{2} \cdot 503 \)	\( - 2^{4} \cdot 11^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$68640$	$0.629271$	$-389017/8048$	$0.80210$	$2.63570$	$[1, 0, 0, -184, -5840]$	\(y^2+xy=x^3-184x-5840\)	1006.2.0.?	$[]$
170014.j1	170014d1	170014.j	170014d	$1$	$1$	\( 2 \cdot 13^{2} \cdot 503 \)	\( - 2^{4} \cdot 13^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$107712$	$0.712798$	$-389017/8048$	$0.80210$	$2.64581$	$[1, 0, 0, -257, 9593]$	\(y^2+xy=x^3-257x+9593\)	1006.2.0.?	$[]$
201200.y1	201200p1	201200.y	201200p	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 503 \)	\( - 2^{16} \cdot 5^{6} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$5.118742329$	$1$		$6$	$147456$	$0.928189$	$-389017/8048$	$0.80210$	$2.82097$	$[0, 1, 0, -608, -35212]$	\(y^2=x^3+x^2-608x-35212\)	1006.2.0.?	$[(218, 3200), (122, 1312)]$
226350.e1	226350bo1	226350.e	226350bo	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 503 \)	\( - 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$184320$	$0.784348$	$-389017/8048$	$0.80210$	$2.65403$	$[1, -1, 0, -342, -14684]$	\(y^2+xy=x^3-x^2-342x-14684\)	1006.2.0.?	$[]$
289728.bh1	289728bh1	289728.bh	289728bh	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 503 \)	\( - 2^{22} \cdot 3^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1.375483270$	$1$		$2$	$276480$	$1.019350$	$-389017/8048$	$0.80210$	$2.82616$	$[0, 0, 0, -876, 60496]$	\(y^2=x^3-876x+60496\)	1006.2.0.?	$[(-6, 256)]$
289728.bi1	289728bi1	289728.bi	289728bi	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 503 \)	\( - 2^{22} \cdot 3^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$5.055403174$	$1$		$0$	$276480$	$1.019350$	$-389017/8048$	$0.80210$	$2.82616$	$[0, 0, 0, -876, -60496]$	\(y^2=x^3-876x-60496\)	1006.2.0.?	$[(1814/5, 63488/5)]$
290734.b1	290734b1	290734.b	290734b	$1$	$1$	\( 2 \cdot 17^{2} \cdot 503 \)	\( - 2^{4} \cdot 17^{6} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$2.891814959$	$1$		$8$	$236544$	$0.846930$	$-389017/8048$	$0.80210$	$2.66092$	$[1, 1, 0, -439, 21317]$	\(y^2+xy=x^3+x^2-439x+21317\)	1006.2.0.?	$[(1, 144), (-14, 165)]$
363166.j1	363166j1	363166.j	363166j	$1$	$1$	\( 2 \cdot 19^{2} \cdot 503 \)	\( - 2^{4} \cdot 19^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$2.639327811$	$1$		$2$	$345600$	$0.902543$	$-389017/8048$	$0.80210$	$2.66681$	$[1, 1, 1, -549, -30245]$	\(y^2+xy+y=x^3+x^2-549x-30245\)	1006.2.0.?	$[(511, 11296)]$
394352.s1	394352s1	394352.s	394352s	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 503 \)	\( - 2^{16} \cdot 7^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$4.586860471$	$1$		$0$	$435456$	$1.096426$	$-389017/8048$	$0.80210$	$2.83032$	$[0, 1, 0, -1192, 95668]$	\(y^2=x^3+x^2-1192x+95668\)	1006.2.0.?	$[(-482/3, 2528/3)]$
443646.bf1	443646bf1	443646.bf	443646bf	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 503 \)	\( - 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$544320$	$0.952584$	$-389017/8048$	$0.80210$	$2.67194$	$[1, -1, 1, -671, 40695]$	\(y^2+xy+y=x^3-x^2-671x+40695\)	1006.2.0.?	$[]$