Elliptic curve isogeny class 14.1-b over number field \(\Q(\sqrt{42}) \)

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-14.1-b
• Conductor: 14.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 14.1-b over \(\Q(\sqrt{42}) \)

Isogeny class 14.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
14.1-b1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -35476 a - 229804\) , \( 9223680 a + 59776488\bigr] \)
14.1-b2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -116 a - 644\) , \( -3360 a - 21560\bigr] \)
14.1-b3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 924 a + 6096\) , \( 67680 a + 438832\bigr] \)
14.1-b4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -7396 a - 47824\) , \( 708960 a + 4594800\bigr] \)
14.1-b5	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2196 a - 14124\) , \( -145440 a - 942344\bigr] \)
14.1-b6	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -567956 a - 3680684\) , \( 592166400 a + 3837677032\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph