Elliptic curve isogeny class 1344.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1344.1-a
• Conductor: 1344.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1344.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 1344.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1344.1-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 25 a - 72\) , \( 111 a - 328\bigr] \)
1344.1-a2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 48\) , \( 48\bigr] \)
1344.1-a3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -12\) , \( 0\bigr] \)
1344.1-a4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \)
1344.1-a5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -152\) , \( 672\bigr] \)
1344.1-a6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -25 a - 47\) , \( -111 a - 217\bigr] \)

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