Elliptic curves over $\Q$ of conductor 525

Results (14 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
525.a1	525a3	525.a	525a	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3 \cdot 5^{10} \cdot 7 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$840$	$48$	$0$	$1.831221716$	$1$		$4$	$384$	$0.638757$	$157551496201/13125$	$0.96087$	$5.65821$	$[1, 1, 1, -2813, -58594]$	\(y^2+xy+y=x^3+x^2-2813x-58594\)	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.ba.1.2, $\ldots$	$[(-31, 17)]$
525.a2	525a2	525.a	525a	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3^{2} \cdot 5^{8} \cdot 7^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$420$	$48$	$0$	$0.915610858$	$1$		$12$	$192$	$0.292183$	$47045881/11025$	$1.04751$	$4.36237$	$[1, 1, 1, -188, -844]$	\(y^2+xy+y=x^3+x^2-188x-844\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.a.1.2, 84.24.0.?, 420.48.0.?	$[(-6, -8)]$
525.a3	525a1	525.a	525a	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3 \cdot 5^{7} \cdot 7 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$840$	$48$	$0$	$1.831221716$	$1$		$7$	$96$	$-0.054390$	$1771561/105$	$0.96659$	$3.83881$	$[1, 1, 1, -63, 156]$	\(y^2+xy+y=x^3+x^2-63x+156\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.ba.1.4, 168.24.0.?, 210.6.0.?, $\ldots$	$[(6, 3)]$
525.a4	525a4	525.a	525a	$4$	$4$	\( 3 \cdot 5^{2} \cdot 7 \)	\( - 3^{4} \cdot 5^{7} \cdot 7^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$840$	$48$	$0$	$0.457805429$	$1$		$10$	$384$	$0.638757$	$590589719/972405$	$0.94478$	$4.86410$	$[1, 1, 1, 437, -4594]$	\(y^2+xy+y=x^3+x^2+437x-4594\)	2.3.0.a.1, 4.12.0-4.c.1.2, 20.24.0-20.h.1.1, 168.24.0.?, 840.48.0.?	$[(20, 102)]$
525.b1	525d1	525.b	525d	$2$	$2$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3^{3} \cdot 5^{3} \cdot 7 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$420$	$12$	$0$	$0.269236866$	$1$		$9$	$48$	$-0.391218$	$5177717/189$	$0.97949$	$3.23917$	$[1, 0, 0, -18, 27]$	\(y^2+xy=x^3-18x+27\)	2.3.0.a.1, 20.6.0.b.1, 84.6.0.?, 210.6.0.?, 420.12.0.?	$[(3, 0)]$
525.b2	525d2	525.b	525d	$2$	$2$	\( 3 \cdot 5^{2} \cdot 7 \)	\( - 3^{6} \cdot 5^{3} \cdot 7^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$420$	$12$	$0$	$0.134618433$	$1$		$14$	$96$	$-0.044644$	$300763/35721$	$1.11388$	$3.63407$	$[1, 0, 0, 7, 102]$	\(y^2+xy=x^3+7x+102\)	2.3.0.a.1, 20.6.0.a.1, 84.6.0.?, 420.12.0.?	$[(1, 10)]$
525.c1	525c1	525.c	525c	$2$	$2$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3^{3} \cdot 5^{9} \cdot 7 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$420$	$12$	$0$	$2.509806654$	$1$		$3$	$240$	$0.413501$	$5177717/189$	$0.97949$	$4.78092$	$[1, 1, 0, -450, 3375]$	\(y^2+xy=x^3+x^2-450x+3375\)	2.3.0.a.1, 20.6.0.b.1, 84.6.0.?, 210.6.0.?, 420.12.0.?	$[(14, 1)]$
525.c2	525c2	525.c	525c	$2$	$2$	\( 3 \cdot 5^{2} \cdot 7 \)	\( - 3^{6} \cdot 5^{9} \cdot 7^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$420$	$12$	$0$	$1.254903327$	$1$		$4$	$480$	$0.760075$	$300763/35721$	$1.11388$	$5.17583$	$[1, 1, 0, 175, 12750]$	\(y^2+xy=x^3+x^2+175x+12750\)	2.3.0.a.1, 20.6.0.a.1, 84.6.0.?, 420.12.0.?	$[(10, 120)]$
525.d1	525b5	525.d	525b	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3 \cdot 5^{6} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.13	2B	$1680$	$192$	$1$	$1$	$4$	$2$	$0$	$512$	$0.878924$	$53297461115137/147$	$1.05087$	$6.58804$	$[1, 1, 0, -19600, -1064375]$	\(y^2+xy=x^3+x^2-19600x-1064375\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$	$[]$
525.d2	525b3	525.d	525b	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3^{2} \cdot 5^{6} \cdot 7^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.18	2Cs	$840$	$192$	$1$	$1$	$1$		$2$	$256$	$0.532351$	$13027640977/21609$	$1.08149$	$5.26024$	$[1, 1, 0, -1225, -17000]$	\(y^2+xy=x^3+x^2-1225x-17000\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 20.24.0-4.b.1.1, $\ldots$	$[]$
525.d3	525b4	525.d	525b	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3^{8} \cdot 5^{6} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.88	2B	$1680$	$192$	$1$	$1$	$1$		$0$	$256$	$0.532351$	$6570725617/45927$	$1.00160$	$5.15096$	$[1, 1, 0, -975, 11250]$	\(y^2+xy=x^3+x^2-975x+11250\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 20.12.0-4.c.1.2, 28.12.0.h.1, $\ldots$	$[]$
525.d4	525b6	525.d	525b	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \)	\( - 3 \cdot 5^{6} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.90	2B	$1680$	$192$	$1$	$1$	$1$		$0$	$512$	$0.878924$	$-4354703137/17294403$	$1.04266$	$5.41452$	$[1, 1, 0, -850, -27125]$	\(y^2+xy=x^3+x^2-850x-27125\)	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$	$[]$
525.d5	525b2	525.d	525b	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \)	\( 3^{4} \cdot 5^{6} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.10	2Cs	$840$	$192$	$1$	$1$	$1$		$2$	$128$	$0.185777$	$7189057/3969$	$1.14862$	$4.06244$	$[1, 1, 0, -100, -125]$	\(y^2+xy=x^3+x^2-100x-125\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 20.24.0-4.b.1.3, 24.48.0.w.2, $\ldots$	$[]$
525.d6	525b1	525.d	525b	$6$	$8$	\( 3 \cdot 5^{2} \cdot 7 \)	\( - 3^{2} \cdot 5^{6} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.1	2B	$1680$	$192$	$1$	$1$	$1$		$1$	$64$	$-0.160796$	$103823/63$	$0.97868$	$3.38587$	$[1, 1, 0, 25, 0]$	\(y^2+xy=x^3+x^2+25x\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$	$[]$