Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-343.1-c
Conductor 343.1
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 343.1-c over \(\Q(\sqrt{29}) \)

Isogeny class 343.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
343.1-c1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -34 a - 205\) , \( 206 a + 1168\bigr] \)
343.1-c2 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 18 a - 57\) , \( 20 a - 99\bigr] \)
343.1-c3 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -7 a + 13\) , \( -6 a + 13\bigr] \)
343.1-c4 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -59 a - 135\) , \( 305 a + 685\bigr] \)

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