Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-448.4-a
Conductor 448.4
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 448.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 448.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
448.4-a1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \)
448.4-a2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( -138\bigr] \)
448.4-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \)
448.4-a4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 7\) , \( 3 a + 4\bigr] \)
448.4-a5 \( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 4\) , \( -3 a + 7\bigr] \)
448.4-a6 \( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph