Elliptic curve isogeny class 375.1-g over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-375.1-g
• Conductor: 375.1
• Rank: \( 1 \)

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