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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-375.2-a
• 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-a over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
375.2-a1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( a - 4\) , \( a - 1\bigr] \)
375.2-a2	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -34 a - 69\) , \( 112 a + 223\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph