Elliptic curves over $\Q$ of conductor 5265

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

Sort order

Select

Results (20 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
5265.a1	5265d1	5265.a	5265d	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{4} \cdot 5^{4} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.554974443$	$1$		$4$	$4896$	$0.584921$	$15614290980864/1373125$	$[0, 0, 1, -2253, 41158]$	\(y^2+y=x^3-2253x+41158\)
5265.b1	5265g1	5265.b	5265g	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{4} \cdot 5^{7} \cdot 13^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$171360$	$2.415615$	$32553894958643707121664/10770194675703125$	$[0, 0, 1, -2878203, -1878910392]$	\(y^2+y=x^3-2878203x-1878910392\)
5265.c1	5265h1	5265.c	5265h	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{6} \cdot 5^{5} \cdot 13^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.056862474$	$1$		$34$	$4320$	$0.345987$	$1345572864/528125$	$[0, 0, 1, -207, 650]$	\(y^2+y=x^3-207x+650\)
5265.d1	5265a1	5265.d	5265a	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( - 3^{12} \cdot 5 \cdot 13^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1.187277759$	$1$		$4$	$3456$	$0.767481$	$-2146689/142805$	$[1, -1, 1, -218, 13366]$	\(y^2+xy+y=x^3-x^2-218x+13366\)
5265.e1	5265b1	5265.e	5265b	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( - 3^{12} \cdot 5 \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3.835392433$	$1$		$2$	$1080$	$0.224203$	$-2146689/65$	$[1, -1, 1, -218, -1214]$	\(y^2+xy+y=x^3-x^2-218x-1214\)
5265.f1	5265k1	5265.f	5265k	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( - 3^{10} \cdot 5^{4} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.175509063$	$1$		$6$	$1728$	$0.344619$	$-9/8125$	$[1, -1, 1, -2, 1054]$	\(y^2+xy+y=x^3-x^2-2x+1054\)
5265.g1	5265m2	5265.g	5265m	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{10} \cdot 5^{6} \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$1.850887809$	$1$		$0$	$3888$	$0.769206$	$30618648576/203125$	$[0, 0, 1, -2538, -48931]$	\(y^2+y=x^3-2538x-48931\)
5265.g2	5265m1	5265.g	5265m	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{6} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$0.616962603$	$1$		$10$	$1296$	$0.219899$	$1177583616/54925$	$[0, 0, 1, -198, 1028]$	\(y^2+y=x^3-198x+1028\)
5265.h1	5265e2	5265.h	5265e	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{10} \cdot 5^{3} \cdot 13^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$1$	$1$		$0$	$7776$	$1.222286$	$439228746694656/21125$	$[0, 0, 1, -61668, -5894377]$	\(y^2+y=x^3-61668x-5894377\)
5265.h2	5265e1	5265.h	5265e	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{6} \cdot 5 \cdot 13^{6} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$1$	$1$		$2$	$2592$	$0.672979$	$86116663296/24134045$	$[0, 0, 1, -828, -6586]$	\(y^2+y=x^3-828x-6586\)
5265.i1	5265j2	5265.i	5265j	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{12} \cdot 5^{2} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$0.665351444$	$1$		$4$	$3888$	$0.769206$	$1177583616/54925$	$[0, 0, 1, -1782, -27763]$	\(y^2+y=x^3-1782x-27763\)
5265.i2	5265j1	5265.i	5265j	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{4} \cdot 5^{6} \cdot 13 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$1.996054332$	$1$		$4$	$1296$	$0.219899$	$30618648576/203125$	$[0, 0, 1, -282, 1812]$	\(y^2+y=x^3-282x+1812\)
5265.j1	5265i2	5265.j	5265i	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{12} \cdot 5 \cdot 13^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$0.887271526$	$1$		$4$	$7776$	$1.222286$	$86116663296/24134045$	$[0, 0, 1, -7452, 177815]$	\(y^2+y=x^3-7452x+177815\)
5265.j2	5265i1	5265.j	5265i	$2$	$3$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{4} \cdot 5^{3} \cdot 13^{2} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$2.661814578$	$1$		$4$	$2592$	$0.672979$	$439228746694656/21125$	$[0, 0, 1, -6852, 218310]$	\(y^2+y=x^3-6852x+218310\)
5265.k1	5265f1	5265.k	5265f	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( - 3^{4} \cdot 5^{4} \cdot 13 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$576$	$-0.204687$	$-9/8125$	$[1, -1, 0, 0, -39]$	\(y^2+xy=x^3-x^2-39\)
5265.l1	5265n1	5265.l	5265n	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( - 3^{6} \cdot 5 \cdot 13^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.936270652$	$1$		$2$	$1152$	$0.218175$	$-2146689/142805$	$[1, -1, 0, -24, -487]$	\(y^2+xy=x^3-x^2-24x-487\)
5265.m1	5265o1	5265.m	5265o	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( - 3^{6} \cdot 5 \cdot 13 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.478012061$	$1$		$2$	$360$	$-0.325103$	$-2146689/65$	$[1, -1, 0, -24, 53]$	\(y^2+xy=x^3-x^2-24x+53\)
5265.n1	5265c1	5265.n	5265c	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{12} \cdot 5^{5} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$4.360304920$	$1$		$0$	$12960$	$0.895293$	$1345572864/528125$	$[0, 0, 1, -1863, -17557]$	\(y^2+y=x^3-1863x-17557\)
5265.o1	5265l1	5265.o	5265l	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{10} \cdot 5^{7} \cdot 13^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.222963181$	$1$		$0$	$514080$	$2.964920$	$32553894958643707121664/10770194675703125$	$[0, 0, 1, -25903827, 50730580577]$	\(y^2+y=x^3-25903827x+50730580577\)
5265.p1	5265p1	5265.p	5265p	$1$	$1$	\( 3^{4} \cdot 5 \cdot 13 \)	\( 3^{10} \cdot 5^{4} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1.546037838$	$1$		$0$	$14688$	$1.134228$	$15614290980864/1373125$	$[0, 0, 1, -20277, -1111273]$	\(y^2+y=x^3-20277x-1111273\)