Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-870.3-g
Conductor 870.3
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 870.3-g over \(\Q(\sqrt{6}) \)

Isogeny class 870.3-g contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
870.3-g1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -143 a - 348\) , \( 1428 a + 3498\bigr] \)
870.3-g2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2283 a - 5588\) , \( 92480 a + 226530\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph