Elliptic curve isogeny class 30.2-a over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-30.2-a
• Conductor: 30.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 30.2-a over \(\Q(\sqrt{6}) \)

Isogeny class 30.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
30.2-a1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 71 a - 174\) , \( -430 a + 1053\bigr] \)
30.2-a2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -354 a + 866\) , \( -2030 a + 4973\bigr] \)
30.2-a3	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 91 a - 224\) , \( -90 a + 221\bigr] \)
30.2-a4	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 856 a - 2114\) , \( 22410 a - 54859\bigr] \)

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