Elliptic curves over $\Q$ of conductor 1856

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 (22 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
1856.a1	1856p1	1856.a	1856p	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.354841401$	$1$		$4$	$3840$	$0.847372$	$-48707390098512/29$	$[0, 0, 0, -19324, 1033936]$	\(y^2=x^3-19324x+1033936\)
1856.b1	1856o1	1856.b	1856o	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{20} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.729139943$	$1$		$4$	$768$	$0.137492$	$-185193/116$	$[0, 0, 0, -76, -368]$	\(y^2=x^3-76x-368\)
1856.c1	1856e1	1856.c	1856e	$2$	$2$	\( 2^{6} \cdot 29 \)	\( 2^{10} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.21	2B	$1$	$1$		$1$	$240$	$-0.295990$	$5619712/29$	$[0, 1, 0, -37, 75]$	\(y^2=x^3+x^2-37x+75\)
1856.c2	1856e2	1856.c	1856e	$2$	$2$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.12	2B	$1$	$1$		$1$	$480$	$0.050583$	$-35152/841$	$[0, 1, 0, -17, 175]$	\(y^2=x^3+x^2-17x+175\)
1856.d1	1856d1	1856.d	1856d	$2$	$3$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.231052836$	$1$		$18$	$256$	$-0.212746$	$-35152/29$	$[0, -1, 0, -17, 49]$	\(y^2=x^3-x^2-17x+49\)
1856.d2	1856d2	1856.d	1856d	$2$	$3$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29^{3} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.231052836$	$1$		$20$	$768$	$0.336560$	$19600688/24389$	$[0, -1, 0, 143, -751]$	\(y^2=x^3-x^2+143x-751\)
1856.e1	1856c1	1856.e	1856c	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{16} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$256$	$0.155843$	$-55990084/29$	$[0, -1, 0, -321, -2111]$	\(y^2=x^3-x^2-321x-2111\)
1856.f1	1856l2	1856.f	1856l	$2$	$5$	\( 2^{6} \cdot 29 \)	\( - 2^{20} \cdot 29^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$0.179550939$	$1$		$4$	$3840$	$1.386885$	$-10418796526321/82044596$	$[0, -1, 0, -29121, 1935457]$	\(y^2=x^3-x^2-29121x+1935457\)
1856.f2	1856l1	1856.f	1856l	$2$	$5$	\( 2^{6} \cdot 29 \)	\( - 2^{28} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$0.897754698$	$1$		$4$	$768$	$0.582166$	$13651919/29696$	$[0, -1, 0, 319, -3743]$	\(y^2=x^3-x^2+319x-3743\)
1856.g1	1856k1	1856.g	1856k	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{6} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1.266091830$	$1$		$2$	$64$	$-0.693702$	$-64/29$	$[0, -1, 0, 0, -2]$	\(y^2=x^3-x^2-2\)
1856.h1	1856m1	1856.h	1856m	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{16} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.430095295$	$1$		$4$	$256$	$-0.105880$	$48668/29$	$[0, -1, 0, 31, 1]$	\(y^2=x^3-x^2+31x+1\)
1856.i1	1856j1	1856.i	1856j	$2$	$3$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1.387073006$	$1$		$2$	$256$	$-0.212746$	$-35152/29$	$[0, 1, 0, -17, -49]$	\(y^2=x^3+x^2-17x-49\)
1856.i2	1856j2	1856.i	1856j	$2$	$3$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.462357668$	$1$		$2$	$768$	$0.336560$	$19600688/24389$	$[0, 1, 0, 143, 751]$	\(y^2=x^3+x^2+143x+751\)
1856.j1	1856i1	1856.j	1856i	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{16} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.300954901$	$1$		$4$	$256$	$0.155843$	$-55990084/29$	$[0, 1, 0, -321, 2111]$	\(y^2=x^3+x^2-321x+2111\)
1856.k1	1856a2	1856.k	1856a	$2$	$5$	\( 2^{6} \cdot 29 \)	\( - 2^{20} \cdot 29^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$1$	$1$		$0$	$3840$	$1.386885$	$-10418796526321/82044596$	$[0, 1, 0, -29121, -1935457]$	\(y^2=x^3+x^2-29121x-1935457\)
1856.k2	1856a1	1856.k	1856a	$2$	$5$	\( 2^{6} \cdot 29 \)	\( - 2^{28} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$1$	$1$		$0$	$768$	$0.582166$	$13651919/29696$	$[0, 1, 0, 319, 3743]$	\(y^2=x^3+x^2+319x+3743\)
1856.l1	1856h1	1856.l	1856h	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{6} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.892765742$	$1$		$2$	$64$	$-0.693702$	$-64/29$	$[0, 1, 0, 0, 2]$	\(y^2=x^3+x^2+2\)
1856.m1	1856b1	1856.m	1856b	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{16} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$256$	$-0.105880$	$48668/29$	$[0, 1, 0, 31, -1]$	\(y^2=x^3+x^2+31x-1\)
1856.n1	1856n1	1856.n	1856n	$2$	$2$	\( 2^{6} \cdot 29 \)	\( 2^{10} \cdot 29 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.21	2B	$3.929056793$	$1$		$1$	$240$	$-0.295990$	$5619712/29$	$[0, -1, 0, -37, -75]$	\(y^2=x^3-x^2-37x-75\)
1856.n2	1856n2	1856.n	1856n	$2$	$2$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.12	2B	$1.964528396$	$1$		$3$	$480$	$0.050583$	$-35152/841$	$[0, -1, 0, -17, -175]$	\(y^2=x^3-x^2-17x-175\)
1856.o1	1856g1	1856.o	1856g	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{14} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$4$	$2$	$0$	$3840$	$0.847372$	$-48707390098512/29$	$[0, 0, 0, -19324, -1033936]$	\(y^2=x^3-19324x-1033936\)
1856.p1	1856f1	1856.p	1856f	$1$	$1$	\( 2^{6} \cdot 29 \)	\( - 2^{20} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$768$	$0.137492$	$-185193/116$	$[0, 0, 0, -76, 368]$	\(y^2=x^3-76x+368\)