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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-375.1-f
• Conductor: 375.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 375.1-f over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
375.1-f1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 19 a - 47\) , \( 15 a - 37\bigr] \)
375.1-f2	\( \bigl[1\) , \( -a\) , \( 1\) , \( -3117 a - 7635\) , \( 108499 a + 265765\bigr] \)
375.1-f3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 229 a - 562\) , \( 2969 a - 7273\bigr] \)
375.1-f4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 154 a - 387\) , \( 4879 a - 11963\bigr] \)

Rank

Rank: \( 0 \)

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