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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-375.1-d
• 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-d over \(\Q(\sqrt{6}) \)

Isogeny class 375.1-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
375.1-d1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -9 a - 4\) , \( -6 a + 4\bigr] \)
375.1-d2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 356 a - 874\) , \( -178 a + 436\bigr] \)
375.1-d3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -309 a - 764\) , \( -4648 a - 11434\bigr] \)
375.1-d4	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 71 a - 232\) , \( 581 a - 1712\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph