Elliptic curves over $\Q$ of conductor 5225

Results (8 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
5225.a1	5225b3	5225.a	5225b	$4$	$4$	\( 5^{2} \cdot 11 \cdot 19 \)	\( 5^{10} \cdot 11 \cdot 19^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$8360$	$48$	$0$	$1$	$1$		$0$	$423936$	$3.213692$	$116256292809537371612841/15216540068579856875$	$1.02754$	$7.33152$	$[1, -1, 1, -25419730, -43387285978]$	\(y^2+xy+y=x^3-x^2-25419730x-43387285978\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 44.12.0.h.1, 152.12.0.?, $\ldots$	$[]$
5225.a2	5225b2	5225.a	5225b	$4$	$4$	\( 5^{2} \cdot 11 \cdot 19 \)	\( 5^{14} \cdot 11^{2} \cdot 19^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$4180$	$48$	$0$	$1$	$4$	$2$	$2$	$211968$	$2.867115$	$104859453317683374662841/2223652969140625$	$1.04825$	$7.31947$	$[1, -1, 1, -24560355, -46841973478]$	\(y^2+xy+y=x^3-x^2-24560355x-46841973478\)	2.6.0.a.1, 20.12.0-2.a.1.1, 44.12.0.a.1, 76.12.0.?, 220.24.0.?, $\ldots$	$[]$
5225.a3	5225b1	5225.a	5225b	$4$	$4$	\( 5^{2} \cdot 11 \cdot 19 \)	\( 5^{10} \cdot 11 \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$8360$	$48$	$0$	$1$	$4$	$2$	$1$	$105984$	$2.520542$	$104857852278310619039721/47155625$	$1.04825$	$7.31947$	$[1, -1, 1, -24560230, -46842474228]$	\(y^2+xy+y=x^3-x^2-24560230x-46842474228\)	2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 88.12.0.?, 152.12.0.?, $\ldots$	$[]$
5225.a4	5225b4	5225.a	5225b	$4$	$4$	\( 5^{2} \cdot 11 \cdot 19 \)	\( - 5^{22} \cdot 11^{4} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$8360$	$48$	$0$	$1$	$4$	$2$	$0$	$423936$	$3.213692$	$-94256762600623910012361/15323275604248046875$	$1.02668$	$7.33594$	$[1, -1, 1, -23702980, -50264614478]$	\(y^2+xy+y=x^3-x^2-23702980x-50264614478\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 38.6.0.b.1, 76.12.0.?, $\ldots$	$[]$
5225.b1	5225c1	5225.b	5225c	$2$	$3$	\( 5^{2} \cdot 11 \cdot 19 \)	\( - 5^{6} \cdot 11^{3} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$330$	$16$	$0$	$0.378462973$	$1$		$4$	$2592$	$0.616302$	$-2258403328/480491$	$0.89836$	$3.68028$	$[0, -1, 1, -683, 8268]$	\(y^2+y=x^3-x^2-683x+8268\)	3.4.0.a.1, 15.8.0-3.a.1.2, 22.2.0.a.1, 66.8.0.a.1, 330.16.0.?	$[(-4, 104)]$
5225.b2	5225c2	5225.b	5225c	$2$	$3$	\( 5^{2} \cdot 11 \cdot 19 \)	\( - 5^{6} \cdot 11 \cdot 19^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$330$	$16$	$0$	$1.135388919$	$1$		$4$	$7776$	$1.165609$	$790939860992/517504691$	$1.13574$	$4.32802$	$[0, -1, 1, 4817, -48107]$	\(y^2+y=x^3-x^2+4817x-48107\)	3.4.0.a.1, 15.8.0-3.a.1.1, 22.2.0.a.1, 66.8.0.a.1, 330.16.0.?	$[(221, 3429)]$
5225.c1	5225a2	5225.c	5225a	$2$	$2$	\( 5^{2} \cdot 11 \cdot 19 \)	\( 5^{7} \cdot 11^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4180$	$12$	$0$	$2.285502678$	$1$		$2$	$3072$	$0.578675$	$3301293169/218405$	$0.81334$	$3.68805$	$[1, 1, 0, -775, 7500]$	\(y^2+xy=x^3+x^2-775x+7500\)	2.3.0.a.1, 10.6.0.a.1, 836.6.0.?, 4180.12.0.?	$[(-24, 126)]$
5225.c2	5225a1	5225.c	5225a	$2$	$2$	\( 5^{2} \cdot 11 \cdot 19 \)	\( 5^{8} \cdot 11 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4180$	$12$	$0$	$4.571005357$	$1$		$1$	$1536$	$0.232102$	$24137569/5225$	$0.98391$	$3.11357$	$[1, 1, 0, -150, -625]$	\(y^2+xy=x^3+x^2-150x-625\)	2.3.0.a.1, 20.6.0.c.1, 418.6.0.?, 4180.12.0.?	$[(-74/3, 427/3)]$