Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-3872.5-d
Conductor 3872.5
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 3872.5-d over \(\Q(\sqrt{-7}) \)

Isogeny class 3872.5-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
3872.5-d1 \( \bigl[a\) , \( 1\) , \( a\) , \( -48 a - 65\) , \( 352 a - 1185\bigr] \)
3872.5-d2 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -30 a + 117\) , \( 617 a - 1138\bigr] \)
3872.5-d3 \( \bigl[a\) , \( a\) , \( a\) , \( -178 a - 86\) , \( 1188 a - 129\bigr] \)
3872.5-d4 \( \bigl[a\) , \( -1\) , \( a\) , \( -140 a + 299\) , \( -624 a - 1207\bigr] \)
3872.5-d5 \( \bigl[a\) , \( a\) , \( a\) , \( -2738 a - 1366\) , \( 86180 a - 19585\bigr] \)
3872.5-d6 \( \bigl[a\) , \( -1\) , \( a\) , \( -2140 a + 4619\) , \( -46032 a - 77943\bigr] \)

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