Elliptic curve isogeny class 24.1-d over number field \(\Q(\sqrt{42}) \)

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-24.1-d
• Conductor: 24.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{42}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 42 \); class number \(2\).

Elliptic curves in class 24.1-d over \(\Q(\sqrt{42}) \)

Isogeny class 24.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
24.1-d1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \)
24.1-d2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
24.1-d3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \)
24.1-d4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)
24.1-d5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)
24.1-d6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)

Rank

Rank: \( 1 \)

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