Elliptic curve isogeny class 870.4-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-870.4-b
• Conductor: 870.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 870.4-b over \(\Q(\sqrt{6}) \)

Isogeny class 870.4-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
870.4-b1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -6 a - 10\) , \( 14 a + 35\bigr] \)
870.4-b2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -96 a - 230\) , \( 562 a + 1367\bigr] \)
870.4-b3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -86 a - 210\) , \( 710 a + 1731\bigr] \)
870.4-b4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -1356 a - 3390\) , \( 43802 a + 106959\bigr] \)

Rank

Rank: \( 1 \)

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