Elliptic curve isogeny class 363.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-363.1-a
• Conductor: 363.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 363.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 363.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
363.1-a1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -215 a + 613\) , \( 885 a - 2460\bigr] \)
363.1-a2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 60 a - 157\) , \( 115 a - 315\bigr] \)
363.1-a3	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 35 a - 87\) , \( -151 a + 428\bigr] \)
363.1-a4	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 735 a - 2047\) , \( 16369 a - 45702\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph