Elliptic curves over \(\Q(\sqrt{17}) \) of conductor 128.5

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree	Base change curves	\(\Q\)-curves	Torsion structure	CM
Analytic order* of Ш	Cyclic isogeny degree	Isogeny class size	Semistable	j-invariant
Regulator*	Curves per isogeny class	Isogeny class degree	Potential good reduction	Bad primes

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.

Results (32 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
128.5-a1	\(\Q(\sqrt{17}) \)	128.5	128.5-a	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 3\) , \( a + 3\bigr] \)
128.5-a2	\(\Q(\sqrt{17}) \)	128.5	128.5-a	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 9\) , \( -2 a + 3\bigr] \)
128.5-a3	\(\Q(\sqrt{17}) \)	128.5	128.5-a	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 47 a - 126\) , \( -221 a + 563\bigr] \)
128.5-a4	\(\Q(\sqrt{17}) \)	128.5	128.5-a	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 97 a - 256\) , \( 459 a - 1181\bigr] \)
128.5-b1	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -23 a + 42\) , \( -329 a + 864\bigr] \)
128.5-b2	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -89 a + 228\) , \( -57 a + 146\bigr] \)
128.5-b3	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 274 a + 429\) , \( 18518 a + 28917\bigr] \)
128.5-b4	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 2 a - 3\) , \( 14 a - 35\bigr] \)
128.5-b5	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -33 a - 52\) , \( 13 a + 20\bigr] \)
128.5-b6	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 1996 a - 5262\) , \( -72821 a + 185664\bigr] \)
128.5-b7	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 116 a - 342\) , \( -1173 a + 3040\bigr] \)
128.5-b8	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( a - 7\) , \( -7 a - 6\bigr] \)
128.5-b9	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -373 a - 592\) , \( 5721 a + 8920\bigr] \)
128.5-b10	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1898 a - 2967\) , \( 64912 a + 101365\bigr] \)
128.5-b11	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -9 a - 117\) , \( -339 a - 74\bigr] \)
128.5-b12	\(\Q(\sqrt{17}) \)	128.5	128.5-b	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10858 a - 27827\) , \( 698508 a - 1789259\bigr] \)
128.5-c1	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -285 a - 443\) , \( -4041 a - 6307\bigr] \)
128.5-c2	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 4\) , \( a + 2\bigr] \)
128.5-c3	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 24 a - 41\) , \( -98 a + 129\bigr] \)
128.5-c4	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a + 32\) , \( 0\bigr] \)
128.5-c5	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 9 a - 24\) , \( 15 a - 41\bigr] \)
128.5-c6	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2431 a - 3923\) , \( 73584 a + 115495\bigr] \)
128.5-c7	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -791 a - 1243\) , \( -16960 a - 26473\bigr] \)
128.5-c8	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 146 a - 374\) , \( 0\bigr] \)
128.5-c9	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 149 a - 404\) , \( 1359 a - 3561\bigr] \)
128.5-c10	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 24 a - 179\) , \( -493 a + 579\bigr] \)
128.5-c11	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1656 a - 4244\) , \( -51666 a + 132346\bigr] \)
128.5-c12	\(\Q(\sqrt{17}) \)	128.5	128.5-c	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -296 a - 1139\) , \( -7277 a - 16189\bigr] \)
128.5-d1	\(\Q(\sqrt{17}) \)	128.5	128.5-d	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a - 1\) , \( -197 a + 505\bigr] \)
128.5-d2	\(\Q(\sqrt{17}) \)	128.5	128.5-d	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -85 a - 133\) , \( -137 a - 214\bigr] \)
128.5-d3	\(\Q(\sqrt{17}) \)	128.5	128.5-d	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a - 7\) , \( a + 2\bigr] \)
128.5-d4	\(\Q(\sqrt{17}) \)	128.5	128.5-d	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -33 a - 57\) , \( 141 a + 214\bigr] \)