Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-870.4-e
Conductor 870.4
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 870.4-e over \(\Q(\sqrt{6}) \)

Isogeny class 870.4-e contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
870.4-e1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -641 a - 2616\) , \( -21320 a - 66336\bigr] \)
870.4-e2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -a - 6\) , \( 120 a + 294\bigr] \)
870.4-e3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -221 a - 566\) , \( 2836 a + 6870\bigr] \)
870.4-e4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -10736 a - 43076\) , \( -1263869 a - 3949200\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph