Properties

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

Related objects

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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-c over \(\Q(\sqrt{42}) \)

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

Curve label Weierstrass Coefficients
14.1-c1 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -8871 a - 57416\) , \( 1135220 a + 7357190\bigr] \)
14.1-c2 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -31 a - 126\) , \( -480 a - 2986\bigr] \)
14.1-c3 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 229 a + 1559\) , \( 8920 a + 57933\bigr] \)
14.1-c4 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -1851 a - 11921\) , \( 84920 a + 550469\bigr] \)
14.1-c5 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -551 a - 3496\) , \( -19280 a - 124824\bigr] \)
14.1-c6 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -141991 a - 920136\) , \( 73736820 a + 477869318\bigr] \)

Rank

Rank: \( 1 \)

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