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

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-14.1-e
• Conductor: 14.1
• Rank: \( 1 \)

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

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

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

Isogeny class 14.1-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
14.1-e1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -14 a - 16\) , \( 8 a + 176\bigr] \)
14.1-e2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -4 a + 49\) , \( -8 a + 73\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph