Properties

Base field \(\Q(\sqrt{42}) \)
Label 2.2.168.1-21.1-c
Conductor 21.1
Rank \( 0 \)

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

Isogeny class 21.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
21.1-c1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1772 a - 11437\) , \( -284098 a + 1841276\bigr] \)
21.1-c2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -48 a + 358\) , \( -248 a + 1718\bigr] \)
21.1-c3 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 212 a - 1327\) , \( -298 a + 2042\bigr] \)
21.1-c4 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2032 a - 13122\) , \( 131652 a - 853092\bigr] \)
21.1-c5 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2552 a - 16492\) , \( -170848 a + 1107332\bigr] \)
21.1-c6 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 40772 a - 264187\) , \( -11291398 a + 73176728\bigr] \)

Rank

Rank: \( 0 \)

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