Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-25.3-a
Conductor 25.3
Rank not recorded

Related objects

Learn more about

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

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

Elliptic curves in class 25.3-a over \(\Q(\sqrt{29}) \)

Isogeny class 25.3-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
25.3-a1 \( \bigl[a\) , \( -1\) , \( a\) , \( 13 a - 53\) , \( 480 a - 1546\bigr] \)
25.3-a2 \( \bigl[a\) , \( -1\) , \( a\) , \( -2 a + 2\) , \( -18 a + 55\bigr] \)
25.3-a3 \( \bigl[1\) , \( -a\) , \( a\) , \( 15 a - 53\) , \( 63 a - 258\bigr] \)
25.3-a4 \( \bigl[1\) , \( -a\) , \( a\) , \( 2\) , \( -2\bigr] \)

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