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

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-32.1-a
• Conductor: 32.1
• Rank bounds: 0...2

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

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

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

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

Curve label	Weierstrass Coefficients
32.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
32.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \)
32.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \)
32.1-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 2\)

Isogeny matrix

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

Isogeny graph