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

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

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
14.1-h1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -48 a - 204\) , \( 272 a + 1976\bigr] \)
14.1-h2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8 a + 56\) , \( -16 a + 112\bigr] \)