Elliptic curves over $\Q$ of conductor 3024

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

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Results (46 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
3024.a1	3024v1	3024.a	3024v	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{17} \cdot 3^{5} \cdot 7^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.076783829$	$1$		$12$	$10080$	$1.263514$	$38983348653/26353376$	$[0, 0, 0, 7053, 93490]$	\(y^2=x^3+7053x+93490\)
3024.b1	3024l1	3024.b	3024l	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{11} \cdot 3^{9} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.164111269$	$1$		$8$	$1440$	$0.300941$	$-54/7$	$[0, 0, 0, -27, 810]$	\(y^2=x^3-27x+810\)
3024.c1	3024r1	3024.c	3024r	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{14} \cdot 3^{3} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$1728$	$0.485786$	$-11527859979/28$	$[0, 0, 0, -2259, -41326]$	\(y^2=x^3-2259x-41326\)
3024.c2	3024r2	3024.c	3024r	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{18} \cdot 3^{9} \cdot 7^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1$	$1$		$0$	$5184$	$1.035093$	$-5000211/21952$	$[0, 0, 0, -1539, -68094]$	\(y^2=x^3-1539x-68094\)
3024.c3	3024r3	3024.c	3024r	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{30} \cdot 3^{11} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$15552$	$1.584398$	$381790581/1835008$	$[0, 0, 0, 13581, 1646514]$	\(y^2=x^3+13581x+1646514\)
3024.d1	3024y2	3024.d	3024y	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{5} \cdot 7^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1.175949099$	$1$		$4$	$864$	$0.222888$	$32710656/343$	$[0, 0, 0, -264, -1636]$	\(y^2=x^3-264x-1636\)
3024.d2	3024y1	3024.d	3024y	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{3} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.391983033$	$1$		$4$	$288$	$-0.326418$	$221184/7$	$[0, 0, 0, -24, 44]$	\(y^2=x^3-24x+44\)
3024.e1	3024q2	3024.e	3024q	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{8} \cdot 3^{11} \cdot 7^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$2592$	$0.686803$	$-2431344/343$	$[0, 0, 0, -999, 13554]$	\(y^2=x^3-999x+13554\)
3024.e2	3024q1	3024.e	3024q	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{8} \cdot 3^{9} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$864$	$0.137496$	$11664/7$	$[0, 0, 0, 81, -54]$	\(y^2=x^3+81x-54\)
3024.f1	3024s3	3024.f	3024s	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{11} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$7776$	$1.251781$	$35184082944/7$	$[0, 0, 0, -61344, 5847984]$	\(y^2=x^3-61344x+5847984\)
3024.f2	3024s2	3024.f	3024s	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{9} \cdot 7^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1$	$1$		$0$	$2592$	$0.702476$	$884736/343$	$[0, 0, 0, -864, 5616]$	\(y^2=x^3-864x+5616\)
3024.f3	3024s1	3024.f	3024s	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{3} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$864$	$0.153169$	$56623104/7$	$[0, 0, 0, -384, -2896]$	\(y^2=x^3-384x-2896\)
3024.g1	3024b1	3024.g	3024b	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{9} \cdot 7^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3.647176246$	$1$		$2$	$2880$	$0.791799$	$36799488/16807$	$[0, 0, 0, -1188, -7236]$	\(y^2=x^3-1188x-7236\)
3024.h1	3024c1	3024.h	3024c	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{10} \cdot 3^{9} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$2.644224464$	$1$		$2$	$576$	$0.307331$	$-78732/7$	$[0, 0, 0, -243, -1566]$	\(y^2=x^3-243x-1566\)
3024.i1	3024d1	3024.i	3024d	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{9} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$576$	$0.157960$	$27648/7$	$[0, 0, 0, -108, -324]$	\(y^2=x^3-108x-324\)
3024.j1	3024k1	3024.j	3024k	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{10} \cdot 3^{9} \cdot 7^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.226528820$	$1$		$8$	$2880$	$0.894528$	$3217428/16807$	$[0, 0, 0, 837, -26406]$	\(y^2=x^3+837x-26406\)
3024.k1	3024u1	3024.k	3024u	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{5} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.186593485$	$1$		$6$	$288$	$-0.147499$	$196608/7$	$[0, 0, 0, -48, 124]$	\(y^2=x^3-48x+124\)
3024.l1	3024bb1	3024.l	3024bb	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{5} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$480$	$0.002885$	$12288/7$	$[0, 0, 0, -48, -16]$	\(y^2=x^3-48x-16\)
3024.m1	3024bc1	3024.m	3024bc	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{14} \cdot 3^{5} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$576$	$0.107499$	$-3/28$	$[0, 0, 0, -3, -254]$	\(y^2=x^3-3x-254\)
3024.n1	3024e1	3024.n	3024e	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{11} \cdot 7^{11} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$31680$	$2.050678$	$116634423954432/1977326743$	$[0, 0, 0, -362988, -82933524]$	\(y^2=x^3-362988x-82933524\)
3024.o1	3024w2	3024.o	3024w	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{13} \cdot 3^{5} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$4.002123776$	$1$		$2$	$2592$	$0.887031$	$-545407363875/14$	$[0, 0, 0, -16995, -852766]$	\(y^2=x^3-16995x-852766\)
3024.o2	3024w1	3024.o	3024w	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{15} \cdot 3^{3} \cdot 7^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1.334041258$	$1$		$4$	$864$	$0.337725$	$-7414875/2744$	$[0, 0, 0, -195, -1342]$	\(y^2=x^3-195x-1342\)
3024.o3	3024w3	3024.o	3024w	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{21} \cdot 3^{9} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$0.444680419$	$1$		$4$	$2592$	$0.887031$	$4492125/3584$	$[0, 0, 0, 1485, 13554]$	\(y^2=x^3+1485x+13554\)
3024.p1	3024m3	3024.p	3024m	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{13} \cdot 3^{11} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$7776$	$1.436337$	$-545407363875/14$	$[0, 0, 0, -152955, 23024682]$	\(y^2=x^3-152955x+23024682\)
3024.p2	3024m2	3024.p	3024m	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{15} \cdot 3^{9} \cdot 7^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1$	$1$		$0$	$2592$	$0.887031$	$-7414875/2744$	$[0, 0, 0, -1755, 36234]$	\(y^2=x^3-1755x+36234\)
3024.p3	3024m1	3024.p	3024m	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{21} \cdot 3^{3} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$864$	$0.337725$	$4492125/3584$	$[0, 0, 0, 165, -502]$	\(y^2=x^3+165x-502\)
3024.q1	3024a1	3024.q	3024a	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{10} \cdot 3^{3} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.551231115$	$1$		$4$	$192$	$-0.241976$	$-78732/7$	$[0, 0, 0, -27, 58]$	\(y^2=x^3-27x+58\)
3024.r1	3024g1	3024.r	3024g	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{3} \cdot 7^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$960$	$0.242492$	$36799488/16807$	$[0, 0, 0, -132, 268]$	\(y^2=x^3-132x+268\)
3024.s1	3024j1	3024.s	3024j	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{5} \cdot 7^{11} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.549407826$	$1$		$2$	$10560$	$1.501371$	$116634423954432/1977326743$	$[0, 0, 0, -40332, 3071612]$	\(y^2=x^3-40332x+3071612\)
3024.t1	3024ba1	3024.t	3024ba	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{14} \cdot 3^{11} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$1728$	$0.656805$	$-3/28$	$[0, 0, 0, -27, 6858]$	\(y^2=x^3-27x+6858\)
3024.u1	3024t1	3024.u	3024t	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{11} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$3.030766875$	$1$		$2$	$1440$	$0.552191$	$12288/7$	$[0, 0, 0, -432, 432]$	\(y^2=x^3-432x+432\)
3024.v1	3024z1	3024.v	3024z	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{11} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$864$	$0.401807$	$196608/7$	$[0, 0, 0, -432, -3348]$	\(y^2=x^3-432x-3348\)
3024.w1	3024h1	3024.w	3024h	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{10} \cdot 3^{3} \cdot 7^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.297908992$	$1$		$4$	$960$	$0.345222$	$3217428/16807$	$[0, 0, 0, 93, 978]$	\(y^2=x^3+93x+978\)
3024.x1	3024i1	3024.x	3024i	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{3} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1.084401280$	$1$		$2$	$192$	$-0.391346$	$27648/7$	$[0, 0, 0, -12, 12]$	\(y^2=x^3-12x+12\)
3024.y1	3024x2	3024.y	3024x	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{5} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$7.035562408$	$1$		$0$	$2592$	$0.702476$	$35184082944/7$	$[0, 0, 0, -6816, -216592]$	\(y^2=x^3-6816x-216592\)
3024.y2	3024x3	3024.y	3024x	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{9} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$0.781729156$	$1$		$2$	$2592$	$0.702476$	$56623104/7$	$[0, 0, 0, -3456, 78192]$	\(y^2=x^3-3456x+78192\)
3024.y3	3024x1	3024.y	3024x	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{12} \cdot 3^{3} \cdot 7^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$2.345187469$	$1$		$2$	$864$	$0.153169$	$884736/343$	$[0, 0, 0, -96, -208]$	\(y^2=x^3-96x-208\)
3024.z1	3024p2	3024.z	3024p	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$864$	$0.137496$	$-2431344/343$	$[0, 0, 0, -111, -502]$	\(y^2=x^3-111x-502\)
3024.z2	3024p1	3024.z	3024p	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{8} \cdot 3^{3} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$288$	$-0.411810$	$11664/7$	$[0, 0, 0, 9, 2]$	\(y^2=x^3+9x+2\)
3024.ba1	3024n2	3024.ba	3024n	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{11} \cdot 7^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$2592$	$0.772194$	$32710656/343$	$[0, 0, 0, -2376, 44172]$	\(y^2=x^3-2376x+44172\)
3024.ba2	3024n1	3024.ba	3024n	$2$	$3$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( 2^{8} \cdot 3^{9} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$864$	$0.222888$	$221184/7$	$[0, 0, 0, -216, -1188]$	\(y^2=x^3-216x-1188\)
3024.bb1	3024o3	3024.bb	3024o	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{14} \cdot 3^{9} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$5184$	$1.035093$	$-11527859979/28$	$[0, 0, 0, -20331, 1115802]$	\(y^2=x^3-20331x+1115802\)
3024.bb2	3024o1	3024.bb	3024o	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{18} \cdot 3^{3} \cdot 7^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1$	$1$		$0$	$1728$	$0.485786$	$-5000211/21952$	$[0, 0, 0, -171, 2522]$	\(y^2=x^3-171x+2522\)
3024.bb3	3024o2	3024.bb	3024o	$3$	$9$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{30} \cdot 3^{5} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$5184$	$1.035093$	$381790581/1835008$	$[0, 0, 0, 1509, -60982]$	\(y^2=x^3+1509x-60982\)
3024.bc1	3024f1	3024.bc	3024f	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{11} \cdot 3^{3} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$480$	$-0.248365$	$-54/7$	$[0, 0, 0, -3, -30]$	\(y^2=x^3-3x-30\)
3024.bd1	3024bd1	3024.bd	3024bd	$1$	$1$	\( 2^{4} \cdot 3^{3} \cdot 7 \)	\( - 2^{17} \cdot 3^{11} \cdot 7^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$30240$	$1.812819$	$38983348653/26353376$	$[0, 0, 0, 63477, -2524230]$	\(y^2=x^3+63477x-2524230\)