Elliptic curves over $\Q$ of conductor 126

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

Sort order

Select

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
126.a1	126b3	126.a	126b	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \)	\( 2^{2} \cdot 3^{8} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.120	2B	$1$	$1$		$0$	$128$	$0.738407$	$268498407453697/252$	$[1, -1, 0, -12096, -509036]$	\(y^2+xy=x^3-x^2-12096x-509036\)
126.a2	126b5	126.a	126b	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \)	\( 2 \cdot 3^{10} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.217	2B	$1$	$1$		$0$	$256$	$1.084980$	$84448510979617/933897762$	$[1, -1, 0, -8226, 286474]$	\(y^2+xy=x^3-x^2-8226x+286474\)
126.a3	126b4	126.a	126b	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \)	\( 2^{2} \cdot 3^{14} \cdot 7^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.96	2Cs	$1$	$1$		$2$	$128$	$0.738407$	$124475734657/63011844$	$[1, -1, 0, -936, -3668]$	\(y^2+xy=x^3-x^2-936x-3668\)
126.a4	126b2	126.a	126b	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \)	\( 2^{4} \cdot 3^{10} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.97	2Cs	$1$	$1$		$2$	$64$	$0.391834$	$65597103937/63504$	$[1, -1, 0, -756, -7808]$	\(y^2+xy=x^3-x^2-756x-7808\)
126.a5	126b1	126.a	126b	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \)	\( - 2^{8} \cdot 3^{8} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.102	2B	$1$	$1$		$1$	$32$	$0.045260$	$-7189057/16128$	$[1, -1, 0, -36, -176]$	\(y^2+xy=x^3-x^2-36x-176\)
126.a6	126b6	126.a	126b	$6$	$8$	\( 2 \cdot 3^{2} \cdot 7 \)	\( - 2 \cdot 3^{22} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.204	2B	$1$	$1$		$0$	$256$	$1.084980$	$6359387729183/4218578658$	$[1, -1, 0, 3474, -31010]$	\(y^2+xy=x^3-x^2+3474x-31010\)
126.b1	126a6	126.b	126a	$6$	$18$	\( 2 \cdot 3^{2} \cdot 7 \)	\( 2^{9} \cdot 3^{6} \cdot 7^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.24.0.1	2B, 3B.1.1	$1$	$1$		$4$	$144$	$0.962407$	$2251439055699625/25088$	$[1, -1, 1, -24575, 1488935]$	\(y^2+xy+y=x^3-x^2-24575x+1488935\)
126.b2	126a5	126.b	126a	$6$	$18$	\( 2 \cdot 3^{2} \cdot 7 \)	\( - 2^{18} \cdot 3^{6} \cdot 7 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.24.0.1	2B, 3B.1.1	$1$	$1$		$5$	$72$	$0.615833$	$-548347731625/1835008$	$[1, -1, 1, -1535, 23591]$	\(y^2+xy+y=x^3-x^2-1535x+23591\)
126.b3	126a4	126.b	126a	$6$	$18$	\( 2 \cdot 3^{2} \cdot 7 \)	\( 2^{3} \cdot 3^{6} \cdot 7^{6} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.24.0.1	2B, 3Cs.1.1	$1$	$1$		$4$	$48$	$0.413101$	$4956477625/941192$	$[1, -1, 1, -320, 1883]$	\(y^2+xy+y=x^3-x^2-320x+1883\)
126.b4	126a2	126.b	126a	$6$	$18$	\( 2 \cdot 3^{2} \cdot 7 \)	\( 2 \cdot 3^{6} \cdot 7^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 9.24.0.3	2B, 3B.1.2	$1$	$1$		$0$	$16$	$-0.136205$	$128787625/98$	$[1, -1, 1, -95, -331]$	\(y^2+xy+y=x^3-x^2-95x-331\)
126.b5	126a1	126.b	126a	$6$	$18$	\( 2 \cdot 3^{2} \cdot 7 \)	\( - 2^{2} \cdot 3^{6} \cdot 7 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 9.24.0.3	2B, 3B.1.2	$1$	$1$		$1$	$8$	$-0.482779$	$-15625/28$	$[1, -1, 1, -5, -7]$	\(y^2+xy+y=x^3-x^2-5x-7\)
126.b6	126a3	126.b	126a	$6$	$18$	\( 2 \cdot 3^{2} \cdot 7 \)	\( - 2^{6} \cdot 3^{6} \cdot 7^{3} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.24.0.1	2B, 3Cs.1.1	$1$	$1$		$5$	$24$	$0.066527$	$9938375/21952$	$[1, -1, 1, 40, 155]$	\(y^2+xy+y=x^3-x^2+40x+155\)