Properties

Base field \(\Q(\sqrt{42}) \)
Label 2.2.168.1-21.1-b
Conductor 21.1
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 21.1-b over \(\Q(\sqrt{42}) \)

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

Curve label Weierstrass Coefficients
21.1-b1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -7084 a - 45802\) , \( 2301132 a + 14913254\bigr] \)
21.1-b2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 196 a + 1378\) , \( 1212 a + 8070\bigr] \)
21.1-b3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -844 a - 5362\) , \( 5772 a + 37622\bigr] \)
21.1-b4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8124 a - 52542\) , \( -1020708 a - 6614730\bigr] \)
21.1-b5 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -10204 a - 66022\) , \( 1407612 a + 9122582\bigr] \)
21.1-b6 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -163084 a - 1056802\) , \( 90983532 a + 589640870\bigr] \)

Rank

Rank not yet determined.

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