Elliptic curves over $\Q$ of conductor 102

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
102.a1	102a1	102.a	102a	$2$	$2$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{2} \cdot 3^{2} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$0.143253892$	$1$		$15$	$8$	$-0.763528$	$1771561/612$	$[1, 1, 0, -2, 0]$	\(y^2+xy=x^3+x^2-2x\)
102.a2	102a2	102.a	102a	$2$	$2$	\( 2 \cdot 3 \cdot 17 \)	\( - 2 \cdot 3^{4} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$0.286507785$	$1$		$8$	$16$	$-0.416955$	$46268279/46818$	$[1, 1, 0, 8, 10]$	\(y^2+xy=x^3+x^2+8x+10\)
102.b1	102c3	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{18} \cdot 3^{2} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.4, 3.8.0.2	2B, 3B.1.2	$1$	$1$		$1$	$72$	$0.641426$	$46753267515625/11591221248$	$[1, 0, 1, -751, -6046]$	\(y^2+xy+y=x^3-751x-6046\)
102.b2	102c1	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{6} \cdot 3^{6} \cdot 17 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.4, 3.8.0.1	2B, 3B.1.1	$1$	$1$		$5$	$24$	$0.092120$	$1845026709625/793152$	$[1, 0, 1, -256, 1550]$	\(y^2+xy+y=x^3-256x+1550\)
102.b3	102c2	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( - 2^{3} \cdot 3^{12} \cdot 17^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.5, 3.8.0.1	2B, 3B.1.1	$1$	$1$		$4$	$48$	$0.438694$	$-1107111813625/1228691592$	$[1, 0, 1, -216, 2062]$	\(y^2+xy+y=x^3-216x+2062\)
102.b4	102c4	102.b	102c	$4$	$6$	\( 2 \cdot 3 \cdot 17 \)	\( - 2^{9} \cdot 3^{4} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.5, 3.8.0.2	2B, 3B.1.2	$1$	$1$		$0$	$144$	$0.988000$	$655215969476375/1001033261568$	$[1, 0, 1, 1809, -37790]$	\(y^2+xy+y=x^3+1809x-37790\)
102.c1	102b5	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2 \cdot 3^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.136	2B	$1$	$4$	$2$	$0$	$128$	$0.847078$	$2361739090258884097/5202$	$[1, 0, 0, -27744, -1781010]$	\(y^2+xy=x^3-27744x-1781010\)
102.c2	102b3	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{2} \cdot 3^{4} \cdot 17^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.48	2Cs	$1$	$1$		$2$	$64$	$0.500504$	$576615941610337/27060804$	$[1, 0, 0, -1734, -27936]$	\(y^2+xy=x^3-1734x-27936\)
102.c3	102b6	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( - 2 \cdot 3^{2} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.165	2B	$1$	$1$		$0$	$128$	$0.847078$	$-491411892194497/125563633938$	$[1, 0, 0, -1644, -30942]$	\(y^2+xy=x^3-1644x-30942\)
102.c4	102b2	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{4} \cdot 3^{8} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.38	2Cs	$1$	$1$		$6$	$32$	$0.153931$	$163936758817/30338064$	$[1, 0, 0, -114, -396]$	\(y^2+xy=x^3-114x-396\)
102.c5	102b1	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( 2^{8} \cdot 3^{4} \cdot 17 \)	$0$	$\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.97	2B	$1$	$1$		$7$	$16$	$-0.192642$	$4354703137/352512$	$[1, 0, 0, -34, 68]$	\(y^2+xy=x^3-34x+68\)
102.c6	102b4	102.c	102b	$6$	$8$	\( 2 \cdot 3 \cdot 17 \)	\( - 2^{2} \cdot 3^{16} \cdot 17 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.99	2B	$1$	$1$		$2$	$64$	$0.500504$	$1276229915423/2927177028$	$[1, 0, 0, 226, -2232]$	\(y^2+xy=x^3+226x-2232\)