Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-175.3-b
Conductor 175.3
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 175.3-b over \(\Q(\sqrt{29}) \)

Isogeny class 175.3-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
175.3-b1 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -223 a - 507\) , \( -3954 a - 8640\bigr] \)
175.3-b2 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 3 a - 5\) , \( 46 a + 111\bigr] \)
175.3-b3 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -7 a - 10\) , \( 3 a + 2\bigr] \)
175.3-b4 \( \bigl[1\) , \( 0\) , \( 0\) , \( 152 a - 487\) , \( -1667 a + 5321\bigr] \)

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