Elliptic curves over \(\Q(\sqrt{10}) \)

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

  *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 (1-50 of 4124 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
6.1-a1	\(\Q(\sqrt{10}) \)	6.1	6.1-a	\( \bigl[a\) , \( a\) , \( 0\) , \( 1263 a - 8032\) , \( 62956 a - 305877\bigr] \)
6.1-a2	\(\Q(\sqrt{10}) \)	6.1	6.1-a	\( \bigl[a\) , \( a\) , \( 0\) , \( 3 a + 8\) , \( 4 a + 3\bigr] \)
6.1-b1	\(\Q(\sqrt{10}) \)	6.1	6.1-b	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 314 a - 2006\) , \( 8873 a - 39813\bigr] \)
6.1-b2	\(\Q(\sqrt{10}) \)	6.1	6.1-b	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 4\) , \( -a - 3\bigr] \)
6.2-a1	\(\Q(\sqrt{10}) \)	6.2	6.2-a	\( \bigl[a\) , \( -a\) , \( a\) , \( -2741954 a - 8670817\) , \( -4394335877 a - 13896110178\bigr] \)
6.2-a2	\(\Q(\sqrt{10}) \)	6.2	6.2-a	\( \bigl[a\) , \( -a\) , \( a\) , \( -374 a - 1177\) , \( -86489 a - 273498\bigr] \)
6.2-b1	\(\Q(\sqrt{10}) \)	6.2	6.2-b	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -315 a - 2006\) , \( -8874 a - 39813\bigr] \)
6.2-b2	\(\Q(\sqrt{10}) \)	6.2	6.2-b	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4\) , \( -3\bigr] \)
12.1-a1	\(\Q(\sqrt{10}) \)	12.1	12.1-a	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a - 42\) , \( 390 a + 1238\bigr] \)
12.1-a2	\(\Q(\sqrt{10}) \)	12.1	12.1-a	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 7\) , \( -3 a - 12\bigr] \)
12.1-a3	\(\Q(\sqrt{10}) \)	12.1	12.1-a	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -34 a - 102\) , \( 162 a + 510\bigr] \)
12.1-a4	\(\Q(\sqrt{10}) \)	12.1	12.1-a	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -534 a - 1682\) , \( 11534 a + 36470\bigr] \)
12.1-b1	\(\Q(\sqrt{10}) \)	12.1	12.1-b	\( \bigl[a\) , \( -a\) , \( a\) , \( -5 a - 11\) , \( 50 a + 161\bigr] \)
12.1-b2	\(\Q(\sqrt{10}) \)	12.1	12.1-b	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a - 39\) , \( a + 5\bigr] \)
12.1-b3	\(\Q(\sqrt{10}) \)	12.1	12.1-b	\( \bigl[a\) , \( -a\) , \( a\) , \( -10 a - 26\) , \( 24 a + 80\bigr] \)
12.1-b4	\(\Q(\sqrt{10}) \)	12.1	12.1-b	\( \bigl[a\) , \( -a\) , \( a\) , \( -135 a - 421\) , \( 1518 a + 4805\bigr] \)
12.2-a1	\(\Q(\sqrt{10}) \)	12.2	12.2-a	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 202 a + 638\) , \( 1306 a + 4130\bigr] \)
12.2-a2	\(\Q(\sqrt{10}) \)	12.2	12.2-a	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -58 a - 182\) , \( 294 a + 930\bigr] \)
12.2-a3	\(\Q(\sqrt{10}) \)	12.2	12.2-a	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -28 a - 87\) , \( -107 a - 338\bigr] \)
12.2-a4	\(\Q(\sqrt{10}) \)	12.2	12.2-a	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -798 a - 2522\) , \( 22946 a + 72562\bigr] \)
12.2-b1	\(\Q(\sqrt{10}) \)	12.2	12.2-b	\( \bigl[a\) , \( a\) , \( a\) , \( 135 a - 421\) , \( -1518 a + 4805\bigr] \)
12.2-b2	\(\Q(\sqrt{10}) \)	12.2	12.2-b	\( \bigl[a\) , \( a\) , \( a\) , \( 10 a - 26\) , \( -24 a + 80\bigr] \)
12.2-b3	\(\Q(\sqrt{10}) \)	12.2	12.2-b	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 39\) , \( -a + 5\bigr] \)
12.2-b4	\(\Q(\sqrt{10}) \)	12.2	12.2-b	\( \bigl[a\) , \( a\) , \( a\) , \( 5 a - 11\) , \( -50 a + 161\bigr] \)
18.2-a1	\(\Q(\sqrt{10}) \)	18.2	18.2-a	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -143 a - 451\) , \( 1462 a + 4623\bigr] \)
18.2-a2	\(\Q(\sqrt{10}) \)	18.2	18.2-a	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 257 a + 814\) , \( 8740 a + 27638\bigr] \)
18.2-b1	\(\Q(\sqrt{10}) \)	18.2	18.2-b	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -4515 a - 14281\) , \( 288657 a + 912811\bigr] \)
18.2-b2	\(\Q(\sqrt{10}) \)	18.2	18.2-b	\( \bigl[a\) , \( -a\) , \( 0\) , \( -65 a - 304\) , \( 1536 a + 4219\bigr] \)
18.2-b3	\(\Q(\sqrt{10}) \)	18.2	18.2-b	\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a - 4\) , \( -12 a - 29\bigr] \)
18.2-b4	\(\Q(\sqrt{10}) \)	18.2	18.2-b	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 15 a + 44\) , \( 114 a + 358\bigr] \)
18.2-c1	\(\Q(\sqrt{10}) \)	18.2	18.2-c	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -95 a + 231\) , \( 6100 a - 19186\bigr] \)
18.2-c2	\(\Q(\sqrt{10}) \)	18.2	18.2-c	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 6220 a - 19669\) , \( 484078 a - 1530789\bigr] \)
18.2-c3	\(\Q(\sqrt{10}) \)	18.2	18.2-c	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65 a + 206\) , \( -203 a + 642\bigr] \)
18.2-c4	\(\Q(\sqrt{10}) \)	18.2	18.2-c	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 25 a - 69\) , \( -104 a + 338\bigr] \)
18.2-d1	\(\Q(\sqrt{10}) \)	18.2	18.2-d	\( \bigl[a\) , \( -a\) , \( a\) , \( 10 a - 39\) , \( -21 a + 66\bigr] \)
18.2-d2	\(\Q(\sqrt{10}) \)	18.2	18.2-d	\( \bigl[a\) , \( -a\) , \( a\) , \( -70 a + 221\) , \( -165 a + 526\bigr] \)
18.3-a1	\(\Q(\sqrt{10}) \)	18.3	18.3-a	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3 a - 12\) , \( a + 2\bigr] \)
18.3-a2	\(\Q(\sqrt{10}) \)	18.3	18.3-a	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 53\) , \( 29 a + 92\bigr] \)
18.3-b1	\(\Q(\sqrt{10}) \)	18.3	18.3-b	\( \bigl[a\) , \( a\) , \( a\) , \( -24882 a - 78689\) , \( -3847743 a - 12167634\bigr] \)
18.3-b2	\(\Q(\sqrt{10}) \)	18.3	18.3-b	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -6 a - 15\) , \( 7 a + 20\bigr] \)
18.3-b3	\(\Q(\sqrt{10}) \)	18.3	18.3-b	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 24 a + 60\) , \( -746 a - 2308\bigr] \)
18.3-b4	\(\Q(\sqrt{10}) \)	18.3	18.3-b	\( \bigl[a\) , \( a\) , \( a\) , \( 258 a + 811\) , \( 1365 a + 4314\bigr] \)
18.3-c1	\(\Q(\sqrt{10}) \)	18.3	18.3-c	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -6220 a - 19669\) , \( -484078 a - 1530789\bigr] \)
18.3-c2	\(\Q(\sqrt{10}) \)	18.3	18.3-c	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -25 a - 69\) , \( 104 a + 338\bigr] \)
18.3-c3	\(\Q(\sqrt{10}) \)	18.3	18.3-c	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 95 a + 231\) , \( -6100 a - 19186\bigr] \)
18.3-c4	\(\Q(\sqrt{10}) \)	18.3	18.3-c	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 65 a + 206\) , \( 203 a + 642\bigr] \)
18.3-d1	\(\Q(\sqrt{10}) \)	18.3	18.3-d	\( \bigl[a\) , \( a\) , \( a\) , \( -10 a - 39\) , \( 21 a + 66\bigr] \)
18.3-d2	\(\Q(\sqrt{10}) \)	18.3	18.3-d	\( \bigl[a\) , \( a\) , \( a\) , \( 70 a + 221\) , \( 165 a + 526\bigr] \)
20.1-a1	\(\Q(\sqrt{10}) \)	20.1	20.1-a	\( \bigl[a\) , \( 1\) , \( 0\) , \( -5\) , \( -25\bigr] \)
20.1-a2	\(\Q(\sqrt{10}) \)	20.1	20.1-a	\( \bigl[a\) , \( 1\) , \( 0\) , \( 5\) , \( 3\bigr] \)