Elliptic curve isogeny class 361.1-c over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-361.1-c
• Conductor: 361.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 361.1-c over \(\Q(\sqrt{6}) \)

Isogeny class 361.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
361.1-c1	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 15386 a - 37695\) , \( -1608548 a + 3940131\bigr] \)
361.1-c2	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 186 a - 455\) , \( -2098 a + 5136\bigr] \)
361.1-c3	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -14 a + 35\) , \( -18 a + 41\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph