Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-2268.2-a
Conductor 2268.2
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 2268.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 2268.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
2268.2-a1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -18 a - 75\) , \( -80 a - 243\bigr] \)
2268.2-a2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 18 a - 93\) , \( 80 a - 323\bigr] \)
2268.2-a3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( -176\bigr] \)
2268.2-a4 \( \bigl[1\) , \( -1\) , \( 0\) , \( 3474\) , \( -31010\bigr] \)
2268.2-a5 \( \bigl[1\) , \( -1\) , \( 0\) , \( -936\) , \( -3668\bigr] \)
2268.2-a6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -8226\) , \( 286474\bigr] \)
2268.2-a7 \( \bigl[1\) , \( -1\) , \( 0\) , \( -756\) , \( -7808\bigr] \)
2268.2-a8 \( \bigl[1\) , \( -1\) , \( 0\) , \( -12096\) , \( -509036\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 16 & 8 & 16 & 4 & 8 \\ 4 & 1 & 2 & 16 & 8 & 16 & 4 & 8 \\ 2 & 2 & 1 & 8 & 4 & 8 & 2 & 4 \\ 16 & 16 & 8 & 1 & 2 & 4 & 4 & 8 \\ 8 & 8 & 4 & 2 & 1 & 2 & 2 & 4 \\ 16 & 16 & 8 & 4 & 2 & 1 & 4 & 8 \\ 4 & 4 & 2 & 4 & 2 & 4 & 1 & 2 \\ 8 & 8 & 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph