Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-1152.7-a
Conductor 1152.7
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 1152.7-a over \(\Q(\sqrt{-7}) \)

Isogeny class 1152.7-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
1152.7-a1 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 2 a - 2\) , \( -4 a - 36\bigr] \)
1152.7-a2 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -13 a - 10\) , \( -23 a + 10\bigr] \)
1152.7-a3 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 5 a + 16\) , \( 21 a - 26\bigr] \)
1152.7-a4 \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -98 a + 138\) , \( -24 a - 776\bigr] \)
1152.7-a5 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 34 a - 22\) , \( -64 a - 32\bigr] \)
1152.7-a6 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 18 a - 50\) , \( 44 a - 148\bigr] \)
1152.7-a7 \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 544 a - 352\) , \( -4498 a - 2042\bigr] \)
1152.7-a8 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 258 a - 770\) , \( 3548 a - 7972\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph