Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-576.1-a
Conductor 576.1
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 576.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 576.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
576.1-a1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -40 a + 105\) , \( 13 a - 35\bigr] \)
576.1-a2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 40 a + 105\) , \( 93 a + 245\bigr] \)
576.1-a3 \( \bigl[0\) , \( -a\) , \( 0\) , \( 120 a - 316\) , \( 1270 a - 3360\bigr] \)
576.1-a4 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -99 a - 271\) , \( -1049 a - 2793\bigr] \)
576.1-a5 \( \bigl[0\) , \( -a\) , \( 0\) , \( -120 a - 316\) , \( 1270 a + 3360\bigr] \)
576.1-a6 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 101 a - 271\) , \( -849 a + 2247\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph