Elliptic curves over \(\Q(\sqrt{15}) \) of conductor 8.1

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 (16 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
8.1-a1	\(\Q(\sqrt{15}) \)	8.1	8.1-a	\( \bigl[0\) , \( a\) , \( 0\) , \( -8 a - 26\) , \( -64 a - 250\bigr] \)
8.1-a2	\(\Q(\sqrt{15}) \)	8.1	8.1-a	\( \bigl[0\) , \( a\) , \( 0\) , \( -208 a - 806\) , \( -1388 a - 5366\bigr] \)
8.1-a3	\(\Q(\sqrt{15}) \)	8.1	8.1-a	\( \bigl[0\) , \( a\) , \( 0\) , \( -168 a - 646\) , \( -2548 a - 9870\bigr] \)
8.1-a4	\(\Q(\sqrt{15}) \)	8.1	8.1-a	\( \bigl[0\) , \( a\) , \( 0\) , \( -2688 a - 10406\) , \( -152764 a - 591654\bigr] \)
8.1-b1	\(\Q(\sqrt{15}) \)	8.1	8.1-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -125 a - 476\) , \( 3263 a + 12642\bigr] \)
8.1-b2	\(\Q(\sqrt{15}) \)	8.1	8.1-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3235 a - 12521\) , \( 67026 a + 259595\bigr] \)
8.1-b3	\(\Q(\sqrt{15}) \)	8.1	8.1-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -2605 a - 10081\) , \( 141300 a + 547257\bigr] \)
8.1-b4	\(\Q(\sqrt{15}) \)	8.1	8.1-b	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -41655 a - 161321\) , \( 9092142 a + 35213719\bigr] \)
8.1-c1	\(\Q(\sqrt{15}) \)	8.1	8.1-c	\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a - 26\) , \( 64 a + 250\bigr] \)
8.1-c2	\(\Q(\sqrt{15}) \)	8.1	8.1-c	\( \bigl[0\) , \( -a\) , \( 0\) , \( -208 a - 806\) , \( 1388 a + 5366\bigr] \)
8.1-c3	\(\Q(\sqrt{15}) \)	8.1	8.1-c	\( \bigl[0\) , \( -a\) , \( 0\) , \( -168 a - 646\) , \( 2548 a + 9870\bigr] \)
8.1-c4	\(\Q(\sqrt{15}) \)	8.1	8.1-c	\( \bigl[0\) , \( -a\) , \( 0\) , \( -2688 a - 10406\) , \( 152764 a + 591654\bigr] \)
8.1-d1	\(\Q(\sqrt{15}) \)	8.1	8.1-d	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -4\) , \( -2\bigr] \)
8.1-d2	\(\Q(\sqrt{15}) \)	8.1	8.1-d	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10 a - 49\) , \( -36 a + 125\bigr] \)
8.1-d3	\(\Q(\sqrt{15}) \)	8.1	8.1-d	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -9\) , \( -2 a - 7\bigr] \)
8.1-d4	\(\Q(\sqrt{15}) \)	8.1	8.1-d	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -10 a - 49\) , \( -56 a - 219\bigr] \)