Properties

Base field \(\Q(\sqrt{51}) \)
Label 2.2.204.1-34.1-a
Conductor 34.1
Rank not recorded

Related objects

Learn more about

Base field \(\Q(\sqrt{51}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 51 \); class number \(2\).

Elliptic curves in class 34.1-a over \(\Q(\sqrt{51}) \)

Isogeny class 34.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
34.1-a1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -3915\) , \( 58374\bigr] \)
34.1-a2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -146475\) , \( -14910426\bigr] \)
34.1-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -55755\) , \( 5066118\bigr] \)
34.1-a4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -133515\) , \( -18775098\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph