Elliptic curve isogeny class 375.2-h over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-375.2-h
• Conductor: 375.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 375.2-h over \(\Q(\sqrt{6}) \)

Isogeny class 375.2-h contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
375.2-h1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -a - 2\) , \( a + 2\bigr] \)
375.2-h2	\( \bigl[a\) , \( -1\) , \( 1\) , \( 6 a - 16\) , \( -5 a + 12\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph