Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-17500.2-b
Conductor 17500.2
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 17500.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 17500.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
17500.2-b1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -150 a - 17\) , \( -900 a + 641\bigr] \)
17500.2-b2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 150 a - 167\) , \( 900 a - 259\bigr] \)
17500.2-b3 \( \bigl[1\) , \( -1\) , \( 0\) , \( 58\) , \( -284\bigr] \)
17500.2-b4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -442\) , \( -2784\bigr] \)
17500.2-b5 \( \bigl[1\) , \( -1\) , \( 0\) , \( -2192\) , \( 37466\bigr] \)
17500.2-b6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -6692\) , \( -209034\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph