Elliptic curve isogeny class 15.2-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-15.2-a
• Conductor: 15.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 15.2-a over \(\Q(\sqrt{21}) \)

Isogeny class 15.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
15.2-a1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -379 a - 681\) , \( 5873 a + 10526\bigr] \)
15.2-a2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 0\) , \( 3 a - 10\bigr] \)
15.2-a3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -64 a - 116\) , \( -387 a - 694\bigr] \)
15.2-a4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -24 a - 41\) , \( 65 a + 116\bigr] \)
15.2-a5	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 40 a - 115\) , \( -74 a + 205\bigr] \)
15.2-a6	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -175 a + 435\) , \( -146 a + 520\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph