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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1792.1-bd
• Conductor: 1792.1
• Rank: \( 1 \)

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

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

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

Isogeny class 1792.1-bd contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1792.1-bd1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 11\) , \( -13 a + 33\bigr] \)
1792.1-bd2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a - 4\) , \( -2 a + 4\bigr] \)
1792.1-bd3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 33 a - 89\) , \( -143 a + 400\bigr] \)
1792.1-bd4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8 a - 24\) , \( 20 a - 56\bigr] \)

Rank

Rank: \( 1 \)

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