Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-375.1-g
Conductor 375.1
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 375.1-g over \(\Q(\sqrt{6}) \)

Isogeny class 375.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
375.1-g1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 2\) , \( 2 a + 5\bigr] \)
375.1-g2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 5 a - 168\) , \( -273 a + 105\bigr] \)
375.1-g3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -10 a - 33\) , \( 30 a + 78\bigr] \)
375.1-g4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -185 a - 458\) , \( 2125 a + 5223\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph