Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.7-v
Conductor 28672.7
Rank \( 1 \)

Related objects

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

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

Elliptic curves in class 28672.7-v over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.7-v contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
28672.7-v1 \( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 34\) , \( -119 a - 54\bigr] \)
28672.7-v2 \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 1\) , \( -a + 4\bigr] \)
28672.7-v3 \( \bigl[0\) , \( a\) , \( 0\) , \( 3 a + 6\) , \( -7 a + 10\bigr] \)
28672.7-v4 \( \bigl[0\) , \( a\) , \( 0\) , \( 43 a + 126\) , \( -439 a + 618\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph