Elliptic curve isogeny class 300.2-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-300.2-b
• Conductor: 300.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 300.2-b over \(\Q(\sqrt{6}) \)

Isogeny class 300.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
300.2-b1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -3\) , \( 3 a + 9\bigr] \)
300.2-b2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -35 a - 68\) , \( 126 a + 291\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph