Properties

Base field \(\Q(\sqrt{42}) \)
Label 2.2.168.1-14.1-k
Conductor 14.1
Rank not recorded

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

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

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

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

Curve label Weierstrass Coefficients
14.1-k1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -23905663 a - 154926339\) , \( -162458649312 a - 1052852380264\bigr] \)
14.1-k2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -73023 a - 473179\) , \( 55263928 a + 358151328\bigr] \)
14.1-k3 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 627937 a + 4069561\) , \( -1156642012 a - 7495896820\bigr] \)
14.1-k4 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4979743 a - 32272359\) , \( -12626975292 a - 81832152532\bigr] \)
14.1-k5 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1474943 a - 9558659\) , \( 2479075808 a + 16066247624\bigr] \)
14.1-k6 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -382797183 a - 2480809219\) , \( -10378740177632 a - 67261923867240\bigr] \)

Rank

Rank not yet determined.

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