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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1792.1-g
• 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-g over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
1792.1-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 6\) , \( -4 a + 11\bigr] \)
1792.1-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 617 a - 1731\) , \( -12688 a + 35410\bigr] \)
1792.1-g3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 37 a - 111\) , \( -200 a + 550\bigr] \)
1792.1-g4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 17 a - 171\) , \( -256 a + 186\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph