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

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-6.1-b
• Conductor: 6.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
6.1-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 15 a - 108\) , \( 220 a - 1443\bigr] \)
6.1-b2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -5 a + 27\) , \( -8 a + 57\bigr] \)
6.1-b3	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -15 a - 33\) , \( -8 a + 249\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph