Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-126.1-f
Conductor 126.1
Rank \( 1 \)

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-f over \(\Q(\sqrt{7}) \)

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

Curve label Weierstrass Coefficients
126.1-f1 \( \bigl[1\) , \( 1\) , \( 1\) , \( 3810 a - 11424\) , \( -224208 a + 611613\bigr] \)
126.1-f2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)
126.1-f3 \( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \)
126.1-f4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \)
126.1-f5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
126.1-f6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
126.1-f7 \( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \)
126.1-f8 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3810 a - 11424\) , \( 224208 a + 611613\bigr] \)

Rank

Rank: \( 1 \)

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