Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-72.1-b
Conductor 72.1
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 72.1-b over \(\Q(\sqrt{7}) \)

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

Curve label Weierstrass Coefficients
72.1-b1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 40 a - 175\) , \( 306 a - 1155\bigr] \)
72.1-b2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
72.1-b3 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 220 a - 555\) , \( -2634 a + 7145\bigr] \)
72.1-b4 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 10 a - 45\) , \( -36 a + 95\bigr] \)
72.1-b5 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -2 a - 5\bigr] \)
72.1-b6 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -40 a - 175\) , \( 226 a + 805\bigr] \)
72.1-b7 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -10 a - 45\) , \( -56 a - 185\bigr] \)
72.1-b8 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -220 a - 555\) , \( -3074 a - 8255\bigr] \)

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