Elliptic curve isogeny class 45.2-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-45.2-a
• Conductor: 45.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 45.2-a over \(\Q(\sqrt{21}) \)

Isogeny class 45.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
45.2-a1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -a + 3\) , \( 2 a - 6\bigr] \)
45.2-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( 2347 a + 4171\) , \( 20528 a + 36708\bigr] \)
45.2-a3	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 239 a - 672\) , \( 3320 a - 9264\bigr] \)
45.2-a4	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 14 a - 42\) , \( 62 a - 174\bigr] \)
45.2-a5	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 224 a - 687\) , \( 3434 a - 9366\bigr] \)
45.2-a6	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 29 a - 132\) , \( -136 a + 264\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph