Elliptic curves over $\Q$ of conductor 1520

Results (19 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
1520.a1	1520e1	1520.a	1520e	$1$	$1$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{11} \cdot 5^{2} \cdot 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152$	$2$	$0$	$0.109123604$	$1$		$12$	$960$	$0.321857$	$-16241202/171475$	$0.93308$	$3.71051$	$[0, 0, 0, -67, -926]$	\(y^2=x^3-67x-926\)	152.2.0.?	$[(53, 380)]$
1520.b1	1520i1	1520.b	1520i	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{4} \cdot 5^{5} \cdot 19^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$760$	$48$	$0$	$2.168876954$	$1$		$3$	$960$	$0.628373$	$5405726654464/407253125$	$0.99078$	$4.38016$	$[0, 1, 0, -921, -10346]$	\(y^2=x^3+x^2-921x-10346\)	2.3.0.a.1, 4.6.0.b.1, 10.6.0.a.1, 20.24.0.e.1, 152.12.0.?, $\ldots$	$[(62, 418)]$
1520.b2	1520i2	1520.b	1520i	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{8} \cdot 5^{10} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$760$	$48$	$0$	$4.337753908$	$1$		$1$	$1920$	$0.974947$	$298091207216/3525390625$	$0.96838$	$4.76805$	$[0, 1, 0, 884, -44280]$	\(y^2=x^3+x^2+884x-44280\)	2.3.0.a.1, 4.6.0.a.1, 20.12.0.d.1, 40.24.0.bc.1, 152.12.0.?, $\ldots$	$[(229/2, 3553/2)]$
1520.c1	1520d2	1520.c	1520d	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{8} \cdot 5 \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$0.859606069$	$1$		$5$	$256$	$-0.220084$	$3631696/1805$	$0.78833$	$2.81860$	$[0, 1, 0, -20, -20]$	\(y^2=x^3+x^2-20x-20\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[(-2, 4)]$
1520.c2	1520d1	1520.c	1520d	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{4} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.719212138$	$1$		$3$	$128$	$-0.566657$	$702464/475$	$0.78481$	$2.21593$	$[0, 1, 0, 5, 0]$	\(y^2=x^3+x^2+5x\)	2.3.0.a.1, 20.6.0.c.1, 38.6.0.b.1, 380.12.0.?	$[(4, 10)]$
1520.d1	1520j2	1520.d	1520j	$2$	$3$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{13} \cdot 5^{2} \cdot 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$456$	$16$	$0$	$0.266274271$	$1$		$8$	$1728$	$1.164286$	$-2376117230685121/342950$	$0.98759$	$5.96768$	$[0, -1, 0, -44480, 3625600]$	\(y^2=x^3-x^2-44480x+3625600\)	3.4.0.a.1, 12.8.0-3.a.1.2, 152.2.0.?, 456.16.0.?	$[(120, 40)]$
1520.d2	1520j1	1520.d	1520j	$2$	$3$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{15} \cdot 5^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$456$	$16$	$0$	$0.088758090$	$1$		$10$	$576$	$0.614980$	$-2992209121/2375000$	$0.90876$	$4.23132$	$[0, -1, 0, -480, 6400]$	\(y^2=x^3-x^2-480x+6400\)	3.4.0.a.1, 12.8.0-3.a.1.1, 152.2.0.?, 456.16.0.?	$[(0, 80)]$
1520.e1	1520f2	1520.e	1520f	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{8} \cdot 5^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$1$	$192$	$-0.105160$	$472058064/475$	$0.91565$	$3.48296$	$[0, 0, 0, -103, 402]$	\(y^2=x^3-103x+402\)	2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 380.12.0.?	$[]$
1520.e2	1520f1	1520.e	1520f	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{4} \cdot 5 \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$1$	$96$	$-0.451734$	$3538944/1805$	$1.20155$	$2.43664$	$[0, 0, 0, -8, 3]$	\(y^2=x^3-8x+3\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[]$
1520.f1	1520b3	1520.f	1520b	$4$	$4$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 5 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$760$	$48$	$0$	$8.014590064$	$1$		$1$	$512$	$0.385319$	$899466517764/95$	$0.96248$	$4.70302$	$[0, 0, 0, -2027, -35126]$	\(y^2=x^3-2027x-35126\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.1, 40.24.0-40.z.1.2, $\ldots$	$[(2089/6, 44605/6)]$
1520.f2	1520b4	1520.f	1520b	$4$	$4$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 5 \cdot 19^{4} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$760$	$48$	$0$	$2.003647516$	$1$		$7$	$512$	$0.385319$	$1263284964/651605$	$0.94894$	$3.80654$	$[0, 0, 0, -227, 434]$	\(y^2=x^3-227x+434\)	2.3.0.a.1, 4.12.0-4.c.1.1, 10.6.0.a.1, 20.24.0-20.g.1.2, 152.24.0.?, $\ldots$	$[(-11, 40)]$
1520.f3	1520b2	1520.f	1520b	$4$	$4$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{8} \cdot 5^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$380$	$48$	$0$	$4.007295032$	$1$		$3$	$256$	$0.038746$	$884901456/9025$	$0.92560$	$3.56873$	$[0, 0, 0, -127, -546]$	\(y^2=x^3-127x-546\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.1, 76.24.0.?, 380.48.0.?	$[(97/2, 825/2)]$
1520.f4	1520b1	1520.f	1520b	$4$	$4$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{4} \cdot 5^{4} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$760$	$48$	$0$	$2.003647516$	$1$		$3$	$128$	$-0.307828$	$-55296/11875$	$1.13186$	$2.67690$	$[0, 0, 0, -2, -21]$	\(y^2=x^3-2x-21\)	2.3.0.a.1, 4.12.0-4.c.1.2, 38.6.0.b.1, 40.24.0-40.z.1.12, 76.24.0.?, $\ldots$	$[(23, 110)]$
1520.g1	1520h1	1520.g	1520h	$1$	$1$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{13} \cdot 5^{2} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152$	$2$	$0$	$0.594651921$	$1$		$4$	$192$	$-0.051817$	$357911/950$	$0.81125$	$3.05509$	$[0, 1, 0, 24, -76]$	\(y^2=x^3+x^2+24x-76\)	152.2.0.?	$[(4, 10)]$
1520.h1	1520c2	1520.h	1520c	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{8} \cdot 5^{7} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$0.593392841$	$1$		$5$	$8960$	$1.622547$	$31248575021659890256/28203125$	$1.01626$	$6.88377$	$[0, -1, 0, -416660, 103658192]$	\(y^2=x^3-x^2-416660x+103658192\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[(364, 300)]$
1520.h2	1520c1	1520.h	1520c	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{4} \cdot 5^{14} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1.186785683$	$1$		$3$	$4480$	$1.275972$	$-121981271658244096/115966796875$	$1.08046$	$5.74859$	$[0, -1, 0, -26035, 1626942]$	\(y^2=x^3-x^2-26035x+1626942\)	2.3.0.a.1, 20.6.0.c.1, 38.6.0.b.1, 380.12.0.?	$[(381/2, 375/2)]$
1520.i1	1520a1	1520.i	1520a	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( 2^{4} \cdot 5^{3} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$1$	$192$	$-0.151219$	$304900096/45125$	$0.86112$	$3.04486$	$[0, -1, 0, -35, -58]$	\(y^2=x^3-x^2-35x-58\)	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[]$
1520.i2	1520a2	1520.i	1520a	$2$	$2$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{8} \cdot 5^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$1$	$384$	$0.195354$	$91765424/296875$	$0.86089$	$3.46741$	$[0, -1, 0, 60, -400]$	\(y^2=x^3-x^2+60x-400\)	2.3.0.a.1, 20.6.0.c.1, 38.6.0.b.1, 380.12.0.?	$[]$
1520.j1	1520g1	1520.j	1520g	$1$	$1$	\( 2^{4} \cdot 5 \cdot 19 \)	\( - 2^{23} \cdot 5^{2} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$152$	$2$	$0$	$1$	$1$		$0$	$2112$	$0.588370$	$-11993263569/972800$	$0.93850$	$4.32085$	$[0, 0, 0, -763, -8662]$	\(y^2=x^3-763x-8662\)	152.2.0.?	$[]$