Elliptic curve isogeny class 81.1-c over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-81.1-c
• Conductor: 81.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.1-c over \(\Q(\sqrt{6}) \)

Isogeny class 81.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
81.1-c1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -14 a + 24\) , \( 22 a - 67\bigr] \)
81.1-c2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( a - 6\) , \( -2 a + 2\bigr] \)
81.1-c3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 136 a - 336\) , \( -1289 a + 3155\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph