Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-3584.4-a
Conductor 3584.4
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 3584.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 3584.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
3584.4-a1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 470 a - 85\) , \( 1671 a + 5005\bigr] \)
3584.4-a2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -53 a - 51\) , \( -336 a - 23\bigr] \)
3584.4-a3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 30 a - 5\) , \( 15 a + 93\bigr] \)
3584.4-a4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -11 a + 1\) , \( -33 a + 39\bigr] \)
3584.4-a5 \( \bigl[0\) , \( 1\) , \( 0\) , \( 5 a - 95\) , \( -99 a - 367\bigr] \)
3584.4-a6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15 a + 25\) , \( -3 a - 47\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph