Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-256.1-h
Conductor 256.1
Rank \( 2 \)

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 256.1-h over \(\Q(\sqrt{29}) \)

Isogeny class 256.1-h contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
256.1-h1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -404 a - 888\) , \( 6724 a + 14760\bigr] \)
256.1-h2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 8\) , \( 4 a + 8\bigr] \)
256.1-h3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 406 a - 1293\) , \( -7129 a + 22777\bigr] \)
256.1-h4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 13\) , \( -9 a + 25\bigr] \)

Rank

Rank: \( 2 \)

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