Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-12800.4-g
Conductor 12800.4
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 12800.4-g over \(\Q(\sqrt{-7}) \)

Isogeny class 12800.4-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
12800.4-g1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 13 a - 26\) , \( -34 a - 68\bigr] \)
12800.4-g2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -7 a + 14\) , \( -6 a - 12\bigr] \)
12800.4-g3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 4\) , \( a + 2\bigr] \)
12800.4-g4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -107 a + 214\) , \( -426 a - 852\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph