Elliptic curves over $\Q$ of conductor 138

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (10 matches)

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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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
138.a1	138a2	138.a	138a	$2$	$2$	\( 2 \cdot 3 \cdot 23 \)	\( 2 \cdot 3 \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$552$	$12$	$0$	$0.354736382$	$1$		$6$	$16$	$-0.404552$	$3463512697/3174$	$0.94552$	$4.45797$	$1$	$[1, 1, 0, -31, 55]$	\(y^2+xy=x^3+x^2-31x+55\)	2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.?	$[(3, -1)]$	$1$
138.a2	138a1	138.a	138a	$2$	$2$	\( 2 \cdot 3 \cdot 23 \)	\( - 2^{2} \cdot 3^{2} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$552$	$12$	$0$	$0.177368191$	$1$		$13$	$8$	$-0.751125$	$-389017/828$	$0.87759$	$2.92541$	$1$	$[1, 1, 0, -1, 1]$	\(y^2+xy=x^3+x^2-x+1\)	2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.?	$[(0, 1)]$	$1$
138.b1	138b4	138.b	138b	$4$	$6$	\( 2 \cdot 3 \cdot 23 \)	\( 2^{6} \cdot 3 \cdot 23^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$276$	$96$	$1$	$1$	$1$		$0$	$96$	$0.696010$	$50591419971625/28422890688$	$1.07125$	$6.40414$	$1$	$[1, 0, 1, -771, 1342]$	\(y^2+xy+y=x^3-771x+1342\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 12.48.0-12.h.1.5, 92.6.0.?, $\ldots$	$[ ]$	$1$
138.b2	138b2	138.b	138b	$4$	$6$	\( 2 \cdot 3 \cdot 23 \)	\( 2^{2} \cdot 3^{3} \cdot 23^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$276$	$96$	$1$	$1$	$1$		$4$	$32$	$0.146704$	$21081759765625/57132$	$1.12484$	$6.22648$	$1$	$[1, 0, 1, -576, 5266]$	\(y^2+xy+y=x^3-576x+5266\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 12.48.0-12.h.1.7, 92.6.0.?, $\ldots$	$[ ]$	$1$
138.b3	138b1	138.b	138b	$4$	$6$	\( 2 \cdot 3 \cdot 23 \)	\( - 2^{4} \cdot 3^{6} \cdot 23 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$276$	$96$	$1$	$1$	$1$		$5$	$16$	$-0.199870$	$-4956477625/268272$	$0.95072$	$4.54886$	$1$	$[1, 0, 1, -36, 82]$	\(y^2+xy+y=x^3-36x+82\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 12.48.0-12.i.1.8, 46.6.0.a.1, $\ldots$	$[ ]$	$1$
138.b4	138b3	138.b	138b	$4$	$6$	\( 2 \cdot 3 \cdot 23 \)	\( - 2^{12} \cdot 3^{2} \cdot 23^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$276$	$96$	$1$	$1$	$1$		$1$	$48$	$0.349436$	$752329532375/448524288$	$1.05431$	$5.55004$	$1$	$[1, 0, 1, 189, 190]$	\(y^2+xy+y=x^3+189x+190\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 12.48.0-12.i.1.6, 46.6.0.a.1, $\ldots$	$[ ]$	$1$
138.c1	138c4	138.c	138c	$4$	$4$	\( 2 \cdot 3 \cdot 23 \)	\( 2 \cdot 3^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.103	2B	$184$	$48$	$0$	$1$	$1$		$0$	$32$	$0.055014$	$1666957239793/301806$	$1.06466$	$5.71150$	$2$	$[1, 1, 1, -247, 1391]$	\(y^2+xy+y=x^3+x^2-247x+1391\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 92.12.0.?, 184.48.0.?	$[ ]$	$1$
138.c2	138c3	138.c	138c	$4$	$4$	\( 2 \cdot 3 \cdot 23 \)	\( 2 \cdot 3^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.58	2B	$184$	$48$	$0$	$1$	$1$		$0$	$32$	$0.055014$	$135559106353/5037138$	$0.97631$	$5.20222$	$2$	$[1, 1, 1, -107, -457]$	\(y^2+xy+y=x^3+x^2-107x-457\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 184.48.0.?	$[ ]$	$1$
138.c3	138c2	138.c	138c	$4$	$4$	\( 2 \cdot 3 \cdot 23 \)	\( 2^{2} \cdot 3^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.1	2Cs	$184$	$48$	$0$	$1$	$1$		$2$	$16$	$-0.291559$	$545338513/171396$	$0.94447$	$4.08278$	$1$	$[1, 1, 1, -17, 11]$	\(y^2+xy+y=x^3+x^2-17x+11\)	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 92.24.0.?, 184.48.0.?	$[ ]$	$1$
138.c4	138c1	138.c	138c	$4$	$4$	\( 2 \cdot 3 \cdot 23 \)	\( - 2^{4} \cdot 3^{2} \cdot 23 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.50	2B	$184$	$48$	$0$	$1$	$1$		$3$	$8$	$-0.638133$	$2924207/3312$	$0.89878$	$3.02167$	$1$	$[1, 1, 1, 3, 3]$	\(y^2+xy+y=x^3+x^2+3x+3\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 46.6.0.a.1, 92.24.0.?, $\ldots$	$[ ]$	$1$

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