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

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-32.1-c
• Conductor: 32.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
32.1-c1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
32.1-c2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \)
32.1-c3	\( \bigl[a\) , \( 0\) , \( a\) , \( 13\) , \( 21\bigr] \)
32.1-c4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 34\) , \( 35\bigr] \)

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