Elliptic curve isogeny class 9.1-c over number field \(\Q(\sqrt{42}) \)

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-9.1-c
• Conductor: 9.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 9.1-c over \(\Q(\sqrt{42}) \)

Isogeny class 9.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
9.1-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -322650 a - 2090997\) , \( 269081541 a + 1743847704\bigr] \)
9.1-c2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 1350 a + 8763\) , \( -1072179 a - 6948504\bigr] \)
9.1-c3	\( \bigl[a\) , \( -a\) , \( 1\) , \( -3720 a - 24009\) , \( -308755 a - 2000780\bigr] \)
9.1-c4	\( \bigl[a\) , \( -a\) , \( 1\) , \( -327720 a - 2123769\) , \( 259525040 a + 1681914670\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph