Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-49.3-d
Conductor 49.3
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 49.3-d over \(\Q(\sqrt{29}) \)

Isogeny class 49.3-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
49.3-d1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 230\) , \( 259 a - 1669\bigr] \)
49.3-d2 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 40 a - 124\) , \( -23 a + 86\bigr] \)
49.3-d3 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -10 a + 31\) , \( 0\bigr] \)
49.3-d4 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -28 a - 75\) , \( -138 a - 355\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph