Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-25.3-c
Conductor 25.3
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 25.3-c over \(\Q(\sqrt{6}) \)

Isogeny class 25.3-c contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
25.3-c1 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -685 a + 1678\) , \( 11772 a - 28836\bigr] \)
25.3-c2 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 3 a + 8\) , \( -13 a - 32\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph