Elliptic curve isogeny class 45.2-b over number field \(\Q(\sqrt{-5}) \)

• Base field: \(\Q(\sqrt{-5}) \)
• Label: 2.0.20.1-45.2-b
• Conductor: 45.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-5}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 5 \); class number \(2\).

Elliptic curves in class 45.2-b over \(\Q(\sqrt{-5}) \)

Isogeny class 45.2-b contains 10 curves linked by isogenies of degrees dividing 32.

Curve label	Weierstrass Coefficients
45.2-b1	\( \bigl[a\) , \( 0\) , \( a\) , \( -395 a + 93\) , \( -2916 a + 8171\bigr] \)
45.2-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( 395 a + 93\) , \( 2916 a + 8171\bigr] \)
45.2-b3	\( \bigl[a\) , \( 0\) , \( a\) , \( -107\) , \( 881\bigr] \)
45.2-b4	\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 1\bigr] \)
45.2-b5	\( \bigl[a\) , \( 0\) , \( a\) , \( 38\) , \( 29\bigr] \)
45.2-b6	\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( 11\bigr] \)
45.2-b7	\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -1\bigr] \)
45.2-b8	\( \bigl[a\) , \( 0\) , \( a\) , \( -132\) , \( 661\bigr] \)
45.2-b9	\( \bigl[a\) , \( 0\) , \( a\) , \( -77\) , \( -241\bigr] \)
45.2-b10	\( \bigl[a\) , \( 0\) , \( a\) , \( -2157\) , \( 39541\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 2 & 32 & 16 & 8 & 16 & 4 & 32 & 8 \\ 4 & 1 & 2 & 32 & 16 & 8 & 16 & 4 & 32 & 8 \\ 2 & 2 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 32 & 32 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 16 & 16 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 8 & 8 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 16 & 16 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 4 & 4 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 32 & 32 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 8 & 8 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph