Elliptic curve isogeny class 500.2-c over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-500.2-c
• Conductor: 500.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 500.2-c over \(\Q(\sqrt{6}) \)

Isogeny class 500.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
500.2-c1	\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -273 a - 682\) , \( 4034 a + 9892\bigr] \)
500.2-c2	\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -3 a - 2\) , \( 10 a + 26\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph