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.e1	1006c1	1006.e	1006c	$1$	$1$	\( 2 \cdot 503 \)	\( - 2^{4} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1006$	$2$	$0$	$0.324915587$	$1$		$4$	$96$	$-0.561197$	$13651919/8048$	$0.83435$	$2.37634$	$[1, 0, 0, 5, 1]$	\(y^2+xy=x^3+5x+1\)	1006.2.0.?	$[(0, 1)]$
8048.b1	8048f1	8048.b	8048f	$1$	$1$	\( 2^{4} \cdot 503 \)	\( - 2^{16} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.822811011$	$1$		$12$	$2304$	$0.131950$	$13651919/8048$	$0.83435$	$2.75177$	$[0, -1, 0, 80, -64]$	\(y^2=x^3-x^2+80x-64\)	1006.2.0.?	$[(8, 32), (2, 10)]$
9054.k1	9054h1	9054.k	9054h	$1$	$1$	\( 2 \cdot 3^{2} \cdot 503 \)	\( - 2^{4} \cdot 3^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$2880$	$-0.011891$	$13651919/8048$	$0.83435$	$2.52674$	$[1, -1, 0, 45, -27]$	\(y^2+xy=x^3-x^2+45x-27\)	1006.2.0.?	$[]$
25150.c1	25150c1	25150.c	25150c	$1$	$1$	\( 2 \cdot 5^{2} \cdot 503 \)	\( - 2^{4} \cdot 5^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.604063357$	$1$		$6$	$7680$	$0.243522$	$13651919/8048$	$0.83435$	$2.57446$	$[1, 1, 0, 125, 125]$	\(y^2+xy=x^3+x^2+125x+125\)	1006.2.0.?	$[(10, 45)]$
32192.n1	32192k1	32192.n	32192k	$1$	$1$	\( 2^{6} \cdot 503 \)	\( - 2^{22} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$18432$	$0.478524$	$13651919/8048$	$0.83435$	$2.78492$	$[0, -1, 0, 319, 193]$	\(y^2=x^3-x^2+319x+193\)	1006.2.0.?	$[]$
32192.y1	32192r1	32192.y	32192r	$1$	$1$	\( 2^{6} \cdot 503 \)	\( - 2^{22} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$18432$	$0.478524$	$13651919/8048$	$0.83435$	$2.78492$	$[0, 1, 0, 319, -193]$	\(y^2=x^3+x^2+319x-193\)	1006.2.0.?	$[]$
49294.e1	49294f1	49294.e	49294f	$1$	$1$	\( 2 \cdot 7^{2} \cdot 503 \)	\( - 2^{4} \cdot 7^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$2.736503299$	$1$		$2$	$36288$	$0.411758$	$13651919/8048$	$0.83435$	$2.60096$	$[1, 1, 1, 244, -99]$	\(y^2+xy+y=x^3+x^2+244x-99\)	1006.2.0.?	$[(15, 77)]$
72432.bw1	72432bx1	72432.bw	72432bx	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 503 \)	\( - 2^{16} \cdot 3^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$69120$	$0.681256$	$13651919/8048$	$0.83435$	$2.80051$	$[0, 0, 0, 717, 1010]$	\(y^2=x^3+717x+1010\)	1006.2.0.?	$[]$
121726.d1	121726a1	121726.d	121726a	$1$	$1$	\( 2 \cdot 11^{2} \cdot 503 \)	\( - 2^{4} \cdot 11^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$129600$	$0.637751$	$13651919/8048$	$0.83435$	$2.63177$	$[1, 0, 1, 602, -728]$	\(y^2+xy+y=x^3+602x-728\)	1006.2.0.?	$[]$
170014.e1	170014j1	170014.e	170014j	$1$	$1$	\( 2 \cdot 13^{2} \cdot 503 \)	\( - 2^{4} \cdot 13^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$215424$	$0.721277$	$13651919/8048$	$0.83435$	$2.64198$	$[1, 0, 1, 841, 1354]$	\(y^2+xy+y=x^3+841x+1354\)	1006.2.0.?	$[]$
201200.z1	201200q1	201200.z	201200q	$1$	$1$	\( 2^{4} \cdot 5^{2} \cdot 503 \)	\( - 2^{16} \cdot 5^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$2.315740308$	$1$		$0$	$184320$	$0.936669$	$13651919/8048$	$0.83435$	$2.81720$	$[0, 1, 0, 1992, -4012]$	\(y^2=x^3+x^2+1992x-4012\)	1006.2.0.?	$[(22/3, 800/3)]$
226350.bm1	226350j1	226350.bm	226350j	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 503 \)	\( - 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$230400$	$0.792828$	$13651919/8048$	$0.83435$	$2.65029$	$[1, -1, 1, 1120, -2253]$	\(y^2+xy+y=x^3-x^2+1120x-2253\)	1006.2.0.?	$[]$
289728.c1	289728c1	289728.c	289728c	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 503 \)	\( - 2^{22} \cdot 3^{6} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$5.917592974$	$1$		$4$	$552960$	$1.027830$	$13651919/8048$	$0.83435$	$2.82250$	$[0, 0, 0, 2868, 8080]$	\(y^2=x^3+2868x+8080\)	1006.2.0.?	$[(18, 256), (108, 1256)]$
289728.d1	289728d1	289728.d	289728d	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 503 \)	\( - 2^{22} \cdot 3^{6} \cdot 503 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$6.234845150$	$1$		$4$	$552960$	$1.027830$	$13651919/8048$	$0.83435$	$2.82250$	$[0, 0, 0, 2868, -8080]$	\(y^2=x^3+2868x-8080\)	1006.2.0.?	$[(110, 1280), (8, 124)]$
290734.e1	290734e1	290734.e	290734e	$1$	$1$	\( 2 \cdot 17^{2} \cdot 503 \)	\( - 2^{4} \cdot 17^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$473088$	$0.855410$	$13651919/8048$	$0.83435$	$2.65725$	$[1, 1, 1, 1439, 3471]$	\(y^2+xy+y=x^3+x^2+1439x+3471\)	1006.2.0.?	$[]$
363166.a1	363166a1	363166.a	363166a	$1$	$1$	\( 2 \cdot 19^{2} \cdot 503 \)	\( - 2^{4} \cdot 19^{6} \cdot 503 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$0.998991883$	$1$		$4$	$691200$	$0.911022$	$13651919/8048$	$0.83435$	$2.66321$	$[1, 1, 0, 1798, -3260]$	\(y^2+xy=x^3+x^2+1798x-3260\)	1006.2.0.?	$[(17, 172)]$
394352.u1	394352u1	394352.u	394352u	$1$	$1$	\( 2^{4} \cdot 7^{2} \cdot 503 \)	\( - 2^{16} \cdot 7^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$4$	$2$	$0$	$870912$	$1.104906$	$13651919/8048$	$0.83435$	$2.82675$	$[0, 1, 0, 3904, 14132]$	\(y^2=x^3+x^2+3904x+14132\)	1006.2.0.?	$[]$
443646.d1	443646d1	443646.d	443646d	$1$	$1$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 503 \)	\( - 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 503 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1006$	$2$	$0$	$1$	$1$		$0$	$1088640$	$0.961064$	$13651919/8048$	$0.83435$	$2.66839$	$[1, -1, 0, 2196, 4864]$	\(y^2+xy=x^3-x^2+2196x+4864\)	1006.2.0.?	$[]$