Elliptic curve isogeny class 400.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-400.1-d
• Conductor: 400.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 400.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 400.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
400.1-d1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a\) , \( -1\bigr] \)
400.1-d2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 10\) , \( 2 a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph