Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-1152.5-a
Conductor 1152.5
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 1152.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 1152.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1152.5-a1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -5 a + 7\) , \( -2 a - 6\bigr] \)
1152.5-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a + 2\) , \( -2 a + 8\bigr] \)
1152.5-a3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 2\) , \( -2 a\bigr] \)
1152.5-a4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 18\) , \( -14 a + 16\bigr] \)

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