Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-14400.4-c
Conductor 14400.4
Rank \( 1 \)

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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 14400.4-c over \(\Q(\sqrt{-7}) \)

Isogeny class 14400.4-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
14400.4-c1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \)
14400.4-c2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \)
14400.4-c3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \)
14400.4-c4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \)
14400.4-c5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
14400.4-c6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph