Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-39204.6-d
Conductor 39204.6
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 39204.6-d over \(\Q(\sqrt{-7}) \)

Isogeny class 39204.6-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
39204.6-d1 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -26 a + 22\) , \( -1195 a - 23\bigr] \)
39204.6-d2 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -8 a - 266\) , \( -209 a - 553\bigr] \)
39204.6-d3 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 100 a + 184\) , \( -551 a + 563\bigr] \)
39204.6-d4 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 1414 a - 1238\) , \( -22975 a - 23\bigr] \)
39204.6-d5 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -308 a + 541\) , \( -1282 a - 4197\bigr] \)
39204.6-d6 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -416 a + 91\) , \( -3320 a + 3969\bigr] \)
39204.6-d7 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -4898 a + 8641\) , \( -85468 a - 264585\bigr] \)
39204.6-d8 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -6626 a + 1441\) , \( -218456 a + 257553\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph