Elliptic curve search results

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 (6 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
18.1-a4	\(\Q(\sqrt{17}) \)	18.1	18.1-a	\( \bigl[1\) , \( a\) , \( a\) , \( 4 a - 9\) , \( -7 a + 17\bigr] \)
144.4-d4	\(\Q(\sqrt{17}) \)	144.4	144.4-d	\( \bigl[a\) , \( a\) , \( 0\) , \( 11 a - 23\) , \( 17 a - 42\bigr] \)
162.1-a4	\(\Q(\sqrt{17}) \)	162.1	162.1-a	\( \bigl[1\) , \( -1\) , \( 0\) , \( 36 a - 93\) , \( 131 a - 335\bigr] \)
288.3-c4	\(\Q(\sqrt{17}) \)	288.3	288.3-c	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 26 a - 66\) , \( -64 a + 164\bigr] \)
576.7-h4	\(\Q(\sqrt{17}) \)	576.7	576.7-h	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -9\) , \( -2 a + 3\bigr] \)
576.7-k4	\(\Q(\sqrt{17}) \)	576.7	576.7-k	\( \bigl[a\) , \( -1\) , \( a\) , \( 124 a - 321\) , \( 875 a - 2243\bigr] \)