Properties

Base field \(\Q(\sqrt{51}) \)
Label 2.2.204.1-24.1-a
Conductor 24.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{51}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 51 \); class number \(2\).

Elliptic curves in class 24.1-a over \(\Q(\sqrt{51}) \)

Isogeny class 24.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
24.1-a1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 141\) , \( -4718\bigr] \)
24.1-a2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 96\) , \( 448\bigr] \)
24.1-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( 70\bigr] \)
24.1-a4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -219\) , \( -1190\bigr] \)
24.1-a5 \( \bigl[0\) , \( 0\) , \( 0\) , \( -579\) , \( 5362\bigr] \)
24.1-a6 \( \bigl[0\) , \( 0\) , \( 0\) , \( -3459\) , \( -78302\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph