Elliptic curve isogeny class 2312.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2312.1-b
• Conductor: 2312.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2312.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 2312.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
2312.1-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -9 a - 13\) , \( -16 a - 27\bigr] \)
2312.1-b2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -49 a - 83\) , \( 214 a + 371\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph