Elliptic curves over \(\Q(\zeta_{7})^+\)

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 2597 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
27.1-a1	\(\Q(\zeta_{7})^+\)	27.1	27.1-a	\( \bigl[0\) , \( -a\) , \( a\) , \( 652 a^{2} - 391 a - 1564\) , \( 10528 a^{2} - 5979 a - 24046\bigr] \)
27.1-a2	\(\Q(\zeta_{7})^+\)	27.1	27.1-a	\( \bigl[0\) , \( -a\) , \( a\) , \( 2 a^{2} - a - 4\) , \( -2 a^{2} + a + 4\bigr] \)
41.1-a1	\(\Q(\zeta_{7})^+\)	41.1	41.1-a	\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 99 a^{2} - 10 a - 348\) , \( 952 a^{2} - 216 a - 2798\bigr] \)
41.1-a2	\(\Q(\zeta_{7})^+\)	41.1	41.1-a	\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( 144 a^{2} - 75 a - 328\) , \( 1172 a^{2} - 646 a - 2650\bigr] \)
41.1-a3	\(\Q(\zeta_{7})^+\)	41.1	41.1-a	\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -a^{2} + 2\) , \( 0\bigr] \)
41.1-a4	\(\Q(\zeta_{7})^+\)	41.1	41.1-a	\( \bigl[1\) , \( -a^{2} + 3\) , \( 1\) , \( -6 a^{2} + 7\) , \( 2 a^{2} + 4 a + 2\bigr] \)
41.2-a1	\(\Q(\zeta_{7})^+\)	41.2	41.2-a	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10 a^{2} - 89 a - 140\) , \( -216 a^{2} - 736 a - 678\bigr] \)
41.2-a2	\(\Q(\zeta_{7})^+\)	41.2	41.2-a	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6 a - 5\) , \( 4 a^{2} - 6 a + 2\bigr] \)
41.2-a3	\(\Q(\zeta_{7})^+\)	41.2	41.2-a	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \)
41.2-a4	\(\Q(\zeta_{7})^+\)	41.2	41.2-a	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -75 a^{2} - 69 a + 35\) , \( -646 a^{2} - 526 a + 340\bigr] \)
41.3-a1	\(\Q(\zeta_{7})^+\)	41.3	41.3-a	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -91 a^{2} + 101 a - 68\) , \( -646 a^{2} + 852 a - 304\bigr] \)
41.3-a2	\(\Q(\zeta_{7})^+\)	41.3	41.3-a	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -71 a^{2} + 146 a - 43\) , \( -456 a^{2} + 1027 a - 381\bigr] \)
41.3-a3	\(\Q(\zeta_{7})^+\)	41.3	41.3-a	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( 4 a^{2} - 4 a - 8\) , \( -11 a^{2} + 7 a + 26\bigr] \)
41.3-a4	\(\Q(\zeta_{7})^+\)	41.3	41.3-a	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -a^{2} + a + 2\) , \( 0\bigr] \)
49.1-a1	\(\Q(\zeta_{7})^+\)	49.1	49.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 62 a^{2} - 26 a - 156\) , \( -380 a^{2} + 192 a + 886\bigr] \)
49.1-a2	\(\Q(\zeta_{7})^+\)	49.1	49.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 2 a^{2} - a - 6\) , \( -9 a^{2} + 4 a + 20\bigr] \)
49.1-a3	\(\Q(\zeta_{7})^+\)	49.1	49.1-a	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
49.1-a4	\(\Q(\zeta_{7})^+\)	49.1	49.1-a	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
56.1-a1	\(\Q(\zeta_{7})^+\)	56.1	56.1-a	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
56.1-a2	\(\Q(\zeta_{7})^+\)	56.1	56.1-a	\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
56.1-a3	\(\Q(\zeta_{7})^+\)	56.1	56.1-a	\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
56.1-a4	\(\Q(\zeta_{7})^+\)	56.1	56.1-a	\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
56.1-a5	\(\Q(\zeta_{7})^+\)	56.1	56.1-a	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
56.1-a6	\(\Q(\zeta_{7})^+\)	56.1	56.1-a	\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)
64.1-a1	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( 1742 a^{2} - 971 a - 3929\) , \( 42399 a^{2} - 23535 a - 95292\bigr] \)
64.1-a2	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( 72 a^{2} + 4 a - 264\) , \( 500 a^{2} - 16 a - 1624\bigr] \)
64.1-a3	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( 102 a^{2} - 61 a - 244\) , \( 640 a^{2} - 360 a - 1460\bigr] \)
64.1-a4	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 131 a - 199\) , \( -6 a^{2} - 855 a - 1073\bigr] \)
64.1-a5	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a^{2} - 11 a - 49\) , \( 55 a^{2} - 31 a - 124\bigr] \)
64.1-a6	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 11 a - 39\) , \( -46 a^{2} + 25 a + 103\bigr] \)
64.1-a7	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a^{2} - a - 4\) , \( 0\bigr] \)
64.1-a8	\(\Q(\zeta_{7})^+\)	64.1	64.1-a	\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a^{2} + 4 a + 16\) , \( 4 a^{2} - 8\bigr] \)
71.1-a1	\(\Q(\zeta_{7})^+\)	71.1	71.1-a	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -190 a^{2} + 410 a - 171\) , \( -2384 a^{2} + 5309 a - 1936\bigr] \)
71.1-a2	\(\Q(\zeta_{7})^+\)	71.1	71.1-a	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -10 a^{2} + 5 a - 26\) , \( -61 a^{2} + 92 a - 76\bigr] \)
71.1-a3	\(\Q(\zeta_{7})^+\)	71.1	71.1-a	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5 a^{2} + 15 a - 11\) , \( 12 a^{2} - 31 a + 15\bigr] \)
71.1-a4	\(\Q(\zeta_{7})^+\)	71.1	71.1-a	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \)
71.2-a1	\(\Q(\zeta_{7})^+\)	71.2	71.2-a	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 410 a^{2} - 221 a - 960\) , \( 5309 a^{2} - 2926 a - 12013\bigr] \)
71.2-a2	\(\Q(\zeta_{7})^+\)	71.2	71.2-a	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 5 a^{2} + 4 a - 50\) , \( 92 a^{2} - 32 a - 290\bigr] \)
71.2-a3	\(\Q(\zeta_{7})^+\)	71.2	71.2-a	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 15 a^{2} - 11 a - 35\) , \( -31 a^{2} + 18 a + 70\bigr] \)
71.2-a4	\(\Q(\zeta_{7})^+\)	71.2	71.2-a	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( -a\) , \( -a^{2} + 1\bigr] \)
71.3-a1	\(\Q(\zeta_{7})^+\)	71.3	71.3-a	\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 4 a^{2} - 10 a - 44\) , \( -32 a^{2} - 61 a - 73\bigr] \)
71.3-a2	\(\Q(\zeta_{7})^+\)	71.3	71.3-a	\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -a^{2} + 1\) , \( 0\bigr] \)
71.3-a3	\(\Q(\zeta_{7})^+\)	71.3	71.3-a	\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -11 a^{2} - 5 a + 6\) , \( 18 a^{2} + 12 a - 9\bigr] \)
71.3-a4	\(\Q(\zeta_{7})^+\)	71.3	71.3-a	\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( -221 a^{2} - 190 a + 81\) , \( -2926 a^{2} - 2384 a + 1532\bigr] \)
91.1-a1	\(\Q(\zeta_{7})^+\)	91.1	91.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -1030 a^{2} + 1620 a - 484\) , \( -21769 a^{2} + 41147 a - 14213\bigr] \)
91.1-a2	\(\Q(\zeta_{7})^+\)	91.1	91.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 15 a^{2} + 5 a - 89\) , \( -89 a^{2} - 20 a + 385\bigr] \)
91.1-a3	\(\Q(\zeta_{7})^+\)	91.1	91.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -4\) , \( -3 a^{2} - a + 9\bigr] \)
91.1-a4	\(\Q(\zeta_{7})^+\)	91.1	91.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -15 a^{2} - 5 a + 1\) , \( -49 a^{2} - 26 a + 29\bigr] \)
91.1-a5	\(\Q(\zeta_{7})^+\)	91.1	91.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 1\) , \( 0\bigr] \)
91.1-a6	\(\Q(\zeta_{7})^+\)	91.1	91.1-a	\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -10 a^{2} - 20 a + 21\) , \( -90 a^{2} + 20 a + 26\bigr] \)