Elliptic curve isogeny class 870.3-c over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-870.3-c
• Conductor: 870.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 870.3-c over \(\Q(\sqrt{6}) \)

Isogeny class 870.3-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
870.3-c1	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 529 a + 1284\) , \( 8335 a + 20391\bigr] \)
870.3-c2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -166 a - 406\) , \( 845 a + 2069\bigr] \)
870.3-c3	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -1181 a - 2896\) , \( -35445 a - 86821\bigr] \)
870.3-c4	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -146 a - 356\) , \( 1315 a + 3221\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph