Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.9-k
Conductor 28672.9
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 28672.9-k over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.9-k contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
28672.9-k1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -11 a - 1\) , \( -18 a + 14\bigr] \)
28672.9-k2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 19\) , \( -74 a + 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph