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

• Base field: \(\Q(\sqrt{42}) \)
• Label: 2.2.168.1-14.1-i
• 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-i over \(\Q(\sqrt{42}) \)

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

Curve label	Weierstrass Coefficients
14.1-i1	\( \bigl[a\) , \( -1\) , \( a\) , \( -36 a - 225\) , \( -2932 a - 18983\bigr] \)
14.1-i2	\( \bigl[a\) , \( -1\) , \( a\) , \( 4 a + 35\) , \( 116 a + 773\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph