Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-14400.1-d
Conductor 14400.1
Rank \( 1 \)

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 14400.1-d over \(\Q(\sqrt{-7}) \)

Isogeny class 14400.1-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
14400.1-d1 \( \bigl[a\) , \( a\) , \( 0\) , \( -550 a - 221\) , \( -14407 a + 5499\bigr] \)
14400.1-d2 \( \bigl[a\) , \( a\) , \( 0\) , \( -1\) , \( 3 a - 1\bigr] \)
14400.1-d3 \( \bigl[a\) , \( a\) , \( 0\) , \( 175 a + 69\) , \( -648 a + 97\bigr] \)
14400.1-d4 \( \bigl[a\) , \( a\) , \( 0\) , \( -50 a - 21\) , \( -117 a + 79\bigr] \)
14400.1-d5 \( \bigl[a\) , \( a\) , \( 0\) , \( -25 a - 11\) , \( 62 a - 3\bigr] \)
14400.1-d6 \( \bigl[a\) , \( a\) , \( 0\) , \( -675 a - 271\) , \( -10542 a + 4229\bigr] \)
14400.1-d7 \( \bigl[a\) , \( a\) , \( 0\) , \( -400 a - 161\) , \( 4517 a - 1293\bigr] \)
14400.1-d8 \( \bigl[a\) , \( a\) , \( 0\) , \( -10800 a - 4321\) , \( -661377 a + 241559\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph