Properties

Base field \(\Q(\sqrt{11}) \)
Label 2.2.44.1-72.1-b
Conductor 72.1
Rank \( 0 \)

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Base field \(\Q(\sqrt{11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 72.1-b over \(\Q(\sqrt{11}) \)

Isogeny class 72.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
72.1-b1 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -234 a + 783\) , \( -25911 a + 85945\bigr] \)
72.1-b2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-b3 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -63 a - 206\) , \( -537 a - 1782\bigr] \)
72.1-b4 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 366 a - 1207\) , \( -6955 a + 23075\bigr] \)
72.1-b5 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 966 a - 3197\) , \( 28759 a - 95375\bigr] \)
72.1-b6 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 5766 a - 19117\) , \( -439639 a + 1458125\bigr] \)

Rank

Rank: \( 0 \)

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