Elliptic curves over $\Q$ of conductor 112

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 (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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
112.a1	112a2	112.a	112a	$2$	$2$	\( 2^{4} \cdot 7 \)	\( 2^{11} \cdot 7^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$0.119959949$	$1$		$15$	$16$	$-0.234669$	$3543122/49$	$[0, 1, 0, -40, 84]$	\(y^2=x^3+x^2-40x+84\)
112.a2	112a1	112.a	112a	$2$	$2$	\( 2^{4} \cdot 7 \)	\( - 2^{10} \cdot 7 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$0.239919898$	$1$		$11$	$8$	$-0.581243$	$-4/7$	$[0, 1, 0, 0, 4]$	\(y^2=x^3+x^2+4\)
112.b1	112b3	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( 2^{11} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.101	2B	$1$	$1$		$1$	$16$	$-0.002033$	$1443468546/7$	$[0, 0, 0, -299, -1990]$	\(y^2=x^3-299x-1990\)
112.b2	112b4	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( 2^{11} \cdot 7^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.49	2B	$1$	$1$		$3$	$16$	$-0.002033$	$11090466/2401$	$[0, 0, 0, -59, 138]$	\(y^2=x^3-59x+138\)
112.b3	112b2	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( 2^{10} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.2	2Cs	$1$	$1$		$3$	$8$	$-0.348607$	$740772/49$	$[0, 0, 0, -19, -30]$	\(y^2=x^3-19x-30\)
112.b4	112b1	112.b	112b	$4$	$4$	\( 2^{4} \cdot 7 \)	\( - 2^{8} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.60	2B	$1$	$1$		$1$	$4$	$-0.695180$	$432/7$	$[0, 0, 0, 1, -2]$	\(y^2=x^3+x-2\)
112.c1	112c6	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( 2^{21} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$144$	$1.106249$	$2251439055699625/25088$	$[0, -1, 0, -43688, 3529328]$	\(y^2=x^3-x^2-43688x+3529328\)
112.c2	112c5	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( - 2^{30} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$72$	$0.759675$	$-548347731625/1835008$	$[0, -1, 0, -2728, 55920]$	\(y^2=x^3-x^2-2728x+55920\)
112.c3	112c4	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( 2^{15} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.12.0.1	2B, 3Cs	$1$	$1$		$1$	$48$	$0.556942$	$4956477625/941192$	$[0, -1, 0, -568, 4464]$	\(y^2=x^3-x^2-568x+4464\)
112.c4	112c2	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( 2^{13} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$16$	$0.007636$	$128787625/98$	$[0, -1, 0, -168, -784]$	\(y^2=x^3-x^2-168x-784\)
112.c5	112c1	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( - 2^{14} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.12.0.1	2B, 3B	$1$	$1$		$1$	$8$	$-0.338938$	$-15625/28$	$[0, -1, 0, -8, -16]$	\(y^2=x^3-x^2-8x-16\)
112.c6	112c3	112.c	112c	$6$	$18$	\( 2^{4} \cdot 7 \)	\( - 2^{18} \cdot 7^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.12.0.1	2B, 3Cs	$1$	$1$		$1$	$24$	$0.210368$	$9938375/21952$	$[0, -1, 0, 72, 368]$	\(y^2=x^3-x^2+72x+368\)