Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-1.1-a
Conductor 1.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 1.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 1.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -3 a - 1\) , \( -2 a - 1\bigr] \)
1.1-a2 \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( a - 1\bigr] \)
1.1-a3 \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 67 a - 161\) , \( 458 a - 1122\bigr] \)
1.1-a4 \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -18 a - 41\) , \( 56 a + 138\bigr] \)
1.1-a5 \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -68 a - 161\) , \( -459 a - 1122\bigr] \)
1.1-a6 \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 17 a - 41\) , \( -57 a + 138\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 6 & 3 & 3 & 6 \\ 2 & 1 & 3 & 6 & 6 & 3 \\ 6 & 3 & 1 & 18 & 2 & 9 \\ 3 & 6 & 18 & 1 & 9 & 2 \\ 3 & 6 & 2 & 9 & 1 & 18 \\ 6 & 3 & 9 & 2 & 18 & 1 \end{array}\right)\)

Isogeny graph