Elliptic curve isogeny class 36.1-g over number field \(\Q(\sqrt{42}) \)

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-36.1-g
• Conductor: 36.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 36.1-g over \(\Q(\sqrt{42}) \)

Isogeny class 36.1-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36.1-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 8\bigr] \)
36.1-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1350 a - 8749\bigr] \)
36.1-g3	\( \bigl[a\) , \( 0\) , \( a\) , \( 12\) , \( 22\bigr] \)
36.1-g4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 780 a - 5055\) , \( 29700 a - 192478\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph