Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-13552.6-c
Conductor 13552.6
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 13552.6-c over \(\Q(\sqrt{-7}) \)

Isogeny class 13552.6-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
13552.6-c1 \( \bigl[a\) , \( -a\) , \( a\) , \( 661 a - 256\) , \( -4844 a - 5221\bigr] \)
13552.6-c2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -96 a + 118\) , \( -35 a + 651\bigr] \)
13552.6-c3 \( \bigl[a\) , \( -a\) , \( a\) , \( 41 a - 16\) , \( -84 a - 69\bigr] \)
13552.6-c4 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -13 a - 25\) , \( 42 a + 14\bigr] \)
13552.6-c5 \( \bigl[a\) , \( 0\) , \( 0\) , \( -16 a + 8\) , \( -48 a + 80\bigr] \)
13552.6-c6 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -23 a + 135\) , \( 384 a + 350\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph