Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-25.2-a
Conductor 25.2
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 25.2-a over \(\Q(\sqrt{6}) \)

Isogeny class 25.2-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
25.2-a1 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( -a - 2\) , \( -a - 3\bigr] \)
25.2-a2 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 19 a - 12\) , \( -31 a + 117\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph