Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-72.1-a
Conductor 72.1
Rank \( 0 \)

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

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

Elliptic curves in class 72.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 72.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
72.1-a1 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 38 a - 175\) , \( -227 a + 805\bigr] \)
72.1-a2 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \)
72.1-a3 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 218 a - 555\) , \( 3073 a - 8255\bigr] \)
72.1-a4 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 8 a - 45\) , \( 55 a - 185\bigr] \)
72.1-a5 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 5\) , \( a - 5\bigr] \)
72.1-a6 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -42 a - 175\) , \( -307 a - 1155\bigr] \)
72.1-a7 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -12 a - 45\) , \( 35 a + 95\bigr] \)
72.1-a8 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -222 a - 555\) , \( 2633 a + 7145\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph