Properties

Base field \(\Q(\sqrt{42}) \)
Label 2.2.168.1-42.1-a
Conductor 42.1
Rank \( 1 \)

Related objects

Learn more about

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

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

Elliptic curves in class 42.1-a over \(\Q(\sqrt{42}) \)

Isogeny class 42.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
42.1-a1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)
42.1-a2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \)
42.1-a3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \)
42.1-a4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
42.1-a5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
42.1-a6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph