Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-175.5-f
Conductor 175.5
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 175.5-f over \(\Q(\sqrt{29}) \)

Isogeny class 175.5-f contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
175.5-f1 \( \bigl[a + 1\) , \( -1\) , \( a\) , \( 193 a - 640\) , \( -2528 a + 8005\bigr] \)
175.5-f2 \( \bigl[a\) , \( 0\) , \( 0\) , \( -2 a - 5\) , \( 2048 a + 4490\bigr] \)
175.5-f3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -37 a + 118\) , \( 0\bigr] \)
175.5-f4 \( \bigl[a + 1\) , \( -1\) , \( a\) , \( 8 a - 50\) , \( -53 a + 105\bigr] \)

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