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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-870.1-s
• Conductor: 870.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
870.1-s1	\( \bigl[1\) , \( -a\) , \( a\) , \( 20 a + 31\) , \( -396 a - 1029\bigr] \)
870.1-s2	\( \bigl[1\) , \( -a\) , \( a\) , \( -5 a - 9\) , \( 9 a + 21\bigr] \)
870.1-s3	\( \bigl[1\) , \( -a\) , \( a\) , \( -25 a - 59\) , \( -81 a - 201\bigr] \)
870.1-s4	\( \bigl[1\) , \( -a\) , \( a\) , \( -390 a - 949\) , \( -6246 a - 15301\bigr] \)

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