Elliptic curve isogeny class 32.1-d over number field \(\Q(\sqrt{42}) \)

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-32.1-d
• Conductor: 32.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 32.1-d over \(\Q(\sqrt{42}) \)

Isogeny class 32.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
32.1-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -208 a + 1348\) , \( 0\bigr] \)
32.1-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 52 a - 337\) , \( 0\bigr] \)
32.1-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 572 a - 3707\) , \( 18900 a - 122486\bigr] \)
32.1-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 572 a - 3707\) , \( -18900 a + 122486\bigr] \)

Rank

Rank: \( 2 \)

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