Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-126.1-a
Conductor 126.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 126.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 126.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
126.1-a1 \( \bigl[a\) , \( 0\) , \( 0\) , \( 3810 a - 11423\) , \( 228018 a - 623037\bigr] \)
126.1-a2 \( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( -9\bigr] \)
126.1-a3 \( \bigl[a\) , \( 0\) , \( 0\) , \( 387\) , \( -891\bigr] \)
126.1-a4 \( \bigl[a\) , \( 0\) , \( 0\) , \( -103\) , \( -205\bigr] \)
126.1-a5 \( \bigl[a\) , \( 0\) , \( 0\) , \( -913\) , \( 10001\bigr] \)
126.1-a6 \( \bigl[a\) , \( 0\) , \( 0\) , \( -83\) , \( -345\bigr] \)
126.1-a7 \( \bigl[a\) , \( 0\) , \( 0\) , \( -1343\) , \( -19749\bigr] \)
126.1-a8 \( \bigl[a\) , \( 0\) , \( 0\) , \( -3810 a - 11423\) , \( -228018 a - 623037\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph