Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-15488.5-d
Conductor 15488.5
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 15488.5-d over \(\Q(\sqrt{-7}) \)

Isogeny class 15488.5-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
15488.5-d1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 6 a + 42\) , \( -33 a + 29\bigr] \)
15488.5-d2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 33 a - 24\) , \( -7 a + 65\bigr] \)
15488.5-d3 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 293 a - 304\) , \( -2575 a + 881\bigr] \)
15488.5-d4 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4 a + 422\) , \( 2375 a - 1363\bigr] \)
15488.5-d5 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 105 a - 72\) , \( -469 a - 43\bigr] \)
15488.5-d6 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 24 a + 126\) , \( 405 a - 487\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph