Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-25.2-a
Conductor 25.2
Rank not recorded

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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 25.2-a over \(\Q(\sqrt{29}) \)

Isogeny class 25.2-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
25.2-a1 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 38\) , \( -64 a - 195\bigr] \)
25.2-a2 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a + 2\) , \( -a - 2\bigr] \)
25.2-a3 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -15 a - 40\) , \( -481 a - 1066\bigr] \)
25.2-a4 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 17 a + 37\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph