Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-7.1-a
Conductor 7.1
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 7.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 7.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
7.1-a1 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 7 a - 18\) , \( 12 a - 37\bigr] \)
7.1-a2 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \)
7.1-a3 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4 a - 8\) , \( -a - 1\bigr] \)
7.1-a4 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 2 a - 28\) , \( 16 a - 33\bigr] \)

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