Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-578.1-b
Conductor 578.1
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 578.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 578.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
578.1-b1 \( \bigl[1\) , \( -a\) , \( a\) , \( -3057 a - 7488\) , \( -141756 a - 347236\bigr] \)
578.1-b2 \( \bigl[1\) , \( -a\) , \( a\) , \( -37 a - 88\) , \( -184 a - 452\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph