Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-324.1-h
Conductor 324.1
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 324.1-h over \(\Q(\sqrt{7}) \)

Isogeny class 324.1-h contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
324.1-h1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \)
324.1-h2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -27\bigr] \)
324.1-h3 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -177 a - 468\) , \( 1688 a + 4466\bigr] \)
324.1-h4 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1617 a - 4278\) , \( -60562 a - 160232\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph