Elliptic curve isogeny class 1792.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1792.1-d
• Conductor: 1792.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1792.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 1792.1-d contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
1792.1-d1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2728\) , \( 55920\bigr] \)
1792.1-d2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( -16\bigr] \)
1792.1-d3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( 368\bigr] \)
1792.1-d4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -568\) , \( 4464\bigr] \)
1792.1-d5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -168\) , \( -784\bigr] \)
1792.1-d6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -43688\) , \( 3529328\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph