Elliptic curves over $\Q$ of conductor 52390

Results (12 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
52390.a1	52390a1	52390.a	52390a	$1$	$1$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{17} \cdot 5 \cdot 13^{10} \cdot 31^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$38.31672564$	$1$		$0$	$21003840$	$3.439003$	$-6856149775935224401/605238722560$	$0.98947$	$6.35177$	$[1, 0, 1, -204454514, -1125337689084]$	\(y^2+xy+y=x^3-204454514x-1125337689084\)	40.2.0.a.1	$[(1260340486684956384/3395357, 1400012656133895839125423108/3395357)]$
52390.b1	52390c4	52390.b	52390c	$4$	$6$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( 2^{2} \cdot 5^{3} \cdot 13^{6} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$24180$	$96$	$1$	$1$	$1$		$0$	$1244160$	$2.211697$	$947226559343329/443751840500$	$0.99256$	$4.58974$	$[1, 0, 1, -345778, 34126848]$	\(y^2+xy+y=x^3-345778x+34126848\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 30.24.0.a.1, $\ldots$	$[]$
52390.b2	52390c2	52390.b	52390c	$4$	$6$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( 2^{6} \cdot 5 \cdot 13^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$24180$	$96$	$1$	$1$	$1$		$0$	$414720$	$1.662390$	$549131937598369/307520$	$0.96644$	$4.53957$	$[1, 0, 1, -288318, 59563376]$	\(y^2+xy+y=x^3-288318x+59563376\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 10.6.0.a.1, 30.24.0.a.1, $\ldots$	$[]$
52390.b3	52390c1	52390.b	52390c	$4$	$6$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{12} \cdot 5^{2} \cdot 13^{6} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$24180$	$96$	$1$	$1$	$1$		$1$	$207360$	$1.315817$	$-131794519969/3174400$	$0.90964$	$3.77629$	$[1, 0, 1, -17918, 940656]$	\(y^2+xy+y=x^3-17918x+940656\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 20.6.0.c.1, 39.8.0-3.a.1.1, $\ldots$	$[]$
52390.b4	52390c3	52390.b	52390c	$4$	$6$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{4} \cdot 5^{6} \cdot 13^{6} \cdot 31^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$24180$	$96$	$1$	$1$	$1$		$1$	$622080$	$1.865124$	$10347405816671/7447750000$	$0.97053$	$4.17407$	$[1, 0, 1, 76722, 4044848]$	\(y^2+xy+y=x^3+76722x+4044848\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 20.6.0.c.1, 39.8.0-3.a.1.2, $\ldots$	$[]$
52390.c1	52390d2	52390.c	52390d	$2$	$2$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( 2^{3} \cdot 5^{2} \cdot 13^{6} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$248$	$12$	$0$	$14.87877170$	$1$		$0$	$225792$	$1.567413$	$133974081659809/192200$	$0.95835$	$4.40974$	$[1, 1, 0, -180157, -29507499]$	\(y^2+xy=x^3+x^2-180157x-29507499\)	2.3.0.a.1, 8.6.0.b.1, 124.6.0.?, 248.12.0.?	$[(5677663/57, 12928099682/57)]$
52390.c2	52390d1	52390.c	52390d	$2$	$2$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{6} \cdot 5^{4} \cdot 13^{6} \cdot 31 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$248$	$12$	$0$	$7.439385852$	$1$		$1$	$112896$	$1.220840$	$-31824875809/1240000$	$0.89741$	$3.64777$	$[1, 1, 0, -11157, -473299]$	\(y^2+xy=x^3+x^2-11157x-473299\)	2.3.0.a.1, 8.6.0.c.1, 62.6.0.b.1, 248.12.0.?	$[(15538/3, 1910513/3)]$
52390.d1	52390b1	52390.d	52390b	$1$	$1$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2 \cdot 5^{8} \cdot 13^{2} \cdot 31^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$248$	$2$	$0$	$6.601634421$	$1$		$0$	$218880$	$1.095743$	$31772115999/23274218750$	$1.00559$	$3.35476$	$[1, -1, 0, 365, 95291]$	\(y^2+xy=x^3-x^2+365x+95291\)	248.2.0.?	$[(13357/12, 1577983/12)]$
52390.e1	52390f1	52390.e	52390f	$1$	$1$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{17} \cdot 5 \cdot 13^{4} \cdot 31^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$1615680$	$2.156528$	$-6856149775935224401/605238722560$	$0.98947$	$4.93551$	$[1, 0, 0, -1209790, -512308668]$	\(y^2+xy=x^3-1209790x-512308668\)	40.2.0.a.1	$[]$
52390.f1	52390e2	52390.f	52390e	$2$	$2$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( 2^{7} \cdot 5 \cdot 13^{10} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$0$	$526848$	$2.100792$	$3989493518355801/17566157440$	$0.99654$	$4.72206$	$[1, -1, 1, -558408, -159859189]$	\(y^2+xy+y=x^3-x^2-558408x-159859189\)	2.3.0.a.1, 40.6.0.b.1, 124.6.0.?, 1240.12.0.?	$[]$
52390.f2	52390e1	52390.f	52390e	$2$	$2$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2^{14} \cdot 5^{2} \cdot 13^{8} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1240$	$12$	$0$	$1$	$1$		$1$	$263424$	$1.754221$	$-125075015001/2145894400$	$0.99480$	$4.08269$	$[1, -1, 1, -17608, -4974069]$	\(y^2+xy+y=x^3-x^2-17608x-4974069\)	2.3.0.a.1, 40.6.0.c.1, 62.6.0.b.1, 1240.12.0.?	$[]$
52390.g1	52390g1	52390.g	52390g	$1$	$1$	\( 2 \cdot 5 \cdot 13^{2} \cdot 31 \)	\( - 2 \cdot 5^{8} \cdot 13^{8} \cdot 31^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$248$	$2$	$0$	$1$	$1$		$0$	$2845440$	$2.378220$	$31772115999/23274218750$	$1.00559$	$4.77102$	$[1, -1, 1, 61653, 209539321]$	\(y^2+xy+y=x^3-x^2+61653x+209539321\)	248.2.0.?	$[]$