Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-16128.5-m
Conductor 16128.5
Rank \( 0 \)

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 16128.5-m over \(\Q(\sqrt{-7}) \)

Isogeny class 16128.5-m contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
16128.5-m1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 193 a - 62\) , \( -766 a - 840\bigr] \)
16128.5-m2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 19 a - 25\) , \( -54 a + 34\bigr] \)
16128.5-m3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 13 a - 2\) , \( -22 a\bigr] \)
16128.5-m4 \( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 16\) , \( -16 a + 4\bigr] \)

Rank

Rank: \( 0 \)

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