Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-25.2-c
Conductor 25.2
Rank \( 0 \)

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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-c over \(\Q(\sqrt{6}) \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph