Elliptic curve isogeny class 870.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-870.1-b
• Conductor: 870.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 870.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 870.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
870.1-b1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 95 a - 230\) , \( -563 a + 1367\bigr] \)
870.1-b2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 5 a - 10\) , \( -15 a + 35\bigr] \)
870.1-b3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 85 a - 210\) , \( -711 a + 1731\bigr] \)
870.1-b4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 1355 a - 3390\) , \( -43803 a + 106959\bigr] \)

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