Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-529.1-b
Conductor 529.1
Rank \( 2 \)

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 529.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 529.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
529.1-b1 \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 27 a - 63\) , \( -109 a + 267\bigr] \)
529.1-b2 \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -28 a - 63\) , \( 108 a + 267\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph