Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.5-j
Conductor 28672.5
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 28672.5-j over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.5-j contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
28672.5-j1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22 a + 7\) , \( -51 a + 79\bigr] \)
28672.5-j2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 11 a - 9\) , \( -21 a - 21\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph