Elliptic curves over $\Q$ of conductor 174

Results (10 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
174.a1	174e1	174.a	174e	$1$	$1$	\( 2 \cdot 3 \cdot 29 \)	\( - 2^{13} \cdot 3 \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$696$	$2$	$0$	$1$	$1$		$0$	$52$	$-0.104838$	$-19968681097/712704$	$0.95286$	$4.60884$	$[1, 1, 0, -56, -192]$	\(y^2+xy=x^3+x^2-56x-192\)	696.2.0.?	$[]$
174.b1	174a1	174.b	174a	$2$	$3$	\( 2 \cdot 3 \cdot 29 \)	\( - 2^{11} \cdot 3^{21} \cdot 29 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$696$	$16$	$0$	$1$	$1$		$2$	$1540$	$1.520357$	$-50577879066661513/621261297432576$	$1.07229$	$8.05642$	$[1, 0, 1, -7705, 1226492]$	\(y^2+xy+y=x^3-7705x+1226492\)	3.8.0-3.a.1.2, 696.16.0.?	$[]$
174.b2	174a2	174.b	174a	$2$	$3$	\( 2 \cdot 3 \cdot 29 \)	\( - 2^{33} \cdot 3^{7} \cdot 29^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$696$	$16$	$0$	$1$	$1$		$0$	$4620$	$2.069664$	$36079072622241241607/458176313589497856$	$1.08854$	$9.31839$	$[1, 0, 1, 68840, -31810330]$	\(y^2+xy+y=x^3+68840x-31810330\)	3.8.0-3.a.1.1, 696.16.0.?	$[]$
174.c1	174d3	174.c	174d	$4$	$4$	\( 2 \cdot 3 \cdot 29 \)	\( 2 \cdot 3^{4} \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.7	2B	$696$	$48$	$0$	$1$	$1$		$0$	$40$	$-0.024261$	$3279392280793/4698$	$0.98780$	$5.58604$	$[1, 0, 1, -310, -2122]$	\(y^2+xy+y=x^3-310x-2122\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 24.24.0-24.y.1.8, 116.12.0.?, $\ldots$	$[]$
174.c2	174d4	174.c	174d	$4$	$4$	\( 2 \cdot 3 \cdot 29 \)	\( 2 \cdot 3 \cdot 29^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.8	2B	$696$	$48$	$0$	$1$	$1$		$0$	$40$	$-0.024261$	$13430356633/4243686$	$0.96374$	$4.52036$	$[1, 0, 1, -50, 86]$	\(y^2+xy+y=x^3-50x+86\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.1, 24.24.0-24.s.1.4, $\ldots$	$[]$
174.c3	174d2	174.c	174d	$4$	$4$	\( 2 \cdot 3 \cdot 29 \)	\( 2^{2} \cdot 3^{2} \cdot 29^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.1	2Cs	$696$	$48$	$0$	$1$	$1$		$2$	$20$	$-0.370835$	$822656953/30276$	$0.92332$	$3.97903$	$[1, 0, 1, -20, -34]$	\(y^2+xy+y=x^3-20x-34\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.b.1.2, 116.12.0.?, $\ldots$	$[]$
174.c4	174d1	174.c	174d	$4$	$4$	\( 2 \cdot 3 \cdot 29 \)	\( - 2^{4} \cdot 3 \cdot 29 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.12	2B	$696$	$48$	$0$	$1$	$1$		$1$	$10$	$-0.717408$	$12167/1392$	$0.93955$	$2.84706$	$[1, 0, 1, 0, -2]$	\(y^2+xy+y=x^3-2\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 24.24.0-24.y.1.2, $\ldots$	$[]$
174.d1	174c1	174.d	174c	$1$	$1$	\( 2 \cdot 3 \cdot 29 \)	\( - 2 \cdot 3^{3} \cdot 29 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$696$	$2$	$0$	$1$	$1$		$0$	$12$	$-0.649752$	$-13997521/1566$	$0.87720$	$3.22368$	$[1, 1, 1, -5, -7]$	\(y^2+xy+y=x^3+x^2-5x-7\)	696.2.0.?	$[]$
174.e1	174b2	174.e	174b	$2$	$7$	\( 2 \cdot 3 \cdot 29 \)	\( - 2 \cdot 3 \cdot 29^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$4872$	$96$	$2$	$1$	$1$		$0$	$196$	$0.977647$	$-30526075007211889/103499257854$	$1.03180$	$7.35856$	$[1, 0, 0, -6511, -203353]$	\(y^2+xy=x^3-6511x-203353\)	7.48.0-7.a.2.2, 696.2.0.?, 4872.96.2.?	$[]$
174.e2	174b1	174.e	174b	$2$	$7$	\( 2 \cdot 3 \cdot 29 \)	\( - 2^{7} \cdot 3^{7} \cdot 29 \)	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$4872$	$96$	$2$	$1$	$1$		$6$	$28$	$0.004691$	$-117649/8118144$	$1.24364$	$4.52880$	$[1, 0, 0, -1, 137]$	\(y^2+xy=x^3-x+137\)	7.48.0-7.a.1.2, 696.2.0.?, 4872.96.2.?	$[]$