Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-44.3-a
Conductor 44.3
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 44.3-a over \(\Q(\sqrt{-7}) \)

Isogeny class 44.3-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
44.3-a1 \( \bigl[1\) , \( a\) , \( 0\) , \( -55 a + 91\) , \( 87 a + 359\bigr] \)
44.3-a2 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -4 a + 40\) , \( 135 a + 83\bigr] \)
44.3-a3 \( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 1\bigr] \)
44.3-a4 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 14 a - 17\) , \( -19 a + 5\bigr] \)
44.3-a5 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( a\) , \( 1\bigr] \)
44.3-a6 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -14 a - 10\) , \( 27 a - 9\bigr] \)
44.3-a7 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -a + 3\) , \( -3 a + 1\bigr] \)
44.3-a8 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 21 a\) , \( 20 a + 57\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 3 & 4 & 6 & 2 & 12 & 12 \\ 4 & 1 & 12 & 4 & 6 & 2 & 12 & 3 \\ 3 & 12 & 1 & 12 & 2 & 6 & 4 & 4 \\ 4 & 4 & 12 & 1 & 6 & 2 & 3 & 12 \\ 6 & 6 & 2 & 6 & 1 & 3 & 2 & 2 \\ 2 & 2 & 6 & 2 & 3 & 1 & 6 & 6 \\ 12 & 12 & 4 & 3 & 2 & 6 & 1 & 4 \\ 12 & 3 & 4 & 12 & 2 & 6 & 4 & 1 \end{array}\right)\)

Isogeny graph