Elliptic curves over \(\Q(\sqrt{5}) \) of conductor 45.1

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	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 (10 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
45.1-a1	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( -4364 \phi - 7739\) , \( -255406 \phi - 296465\bigr] \)
45.1-a2	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)
45.1-a3	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
45.1-a4	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
45.1-a5	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
45.1-a6	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
45.1-a7	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)
45.1-a8	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
45.1-a9	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
45.1-a10	\(\Q(\sqrt{5}) \)	45.1	45.1-a	\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi + 1\) , \( 4364 \phi - 12105\) , \( 243301 \phi - 535402\bigr] \)