Elliptic curve isogeny class 6.1-a over number field \(\Q(\sqrt{42}) \)

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-6.1-a
• Conductor: 6.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 6.1-a over \(\Q(\sqrt{42}) \)

Isogeny class 6.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
6.1-a1	\( \bigl[1\) , \( -a\) , \( 0\) , \( 361 a - 2327\) , \( -7786 a + 50451\bigr] \)
6.1-a2	\( \bigl[1\) , \( -a\) , \( 0\) , \( 81 a - 512\) , \( 1192 a - 7734\bigr] \)
6.1-a3	\( \bigl[1\) , \( -a\) , \( 0\) , \( 6571 a - 42572\) , \( 752882 a - 4879242\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph