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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1344.1-b
• 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-b over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
1344.1-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 13200 a - 40872\) , \( -1359264 a + 3894252\bigr] \)
1344.1-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \)
1344.1-b3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -392\) , \( -228\bigr] \)
1344.1-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -252\) , \( 1620\bigr] \)
1344.1-b5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4032\) , \( 99900\bigr] \)
1344.1-b6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13200 a - 27672\) , \( 1359264 a + 2534988\bigr] \)

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