Elliptic curve isogeny class 80.1-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-80.1-a
• Conductor: 80.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 80.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 80.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
80.1-a1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -466 a - 1175\) , \( -8421 a - 20735\bigr] \)
80.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6 a - 15\) , \( -9 a - 23\bigr] \)
80.1-a3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 34 a + 85\) , \( -17 a - 35\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph