Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-25.1-a
Conductor 25.1
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{29}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 7 \); class number \(1\).

Elliptic curves in class 25.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 25.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
25.1-a1 \( \bigl[a + 1\) , \( -a\) , \( a\) , \( -9 a - 20\) , \( 68 a + 148\bigr] \)
25.1-a2 \( \bigl[a + 1\) , \( -a\) , \( a\) , \( 71 a + 145\) , \( -1764 a - 3893\bigr] \)
25.1-a3 \( \bigl[a + 1\) , \( -a\) , \( a\) , \( -59 a - 140\) , \( -398 a - 898\bigr] \)
25.1-a4 \( \bigl[a + 1\) , \( -a\) , \( a\) , \( -14 a - 30\) , \( 35 a + 76\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph