Elliptic curve isogeny class 2304.1-h over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2304.1-h
• Conductor: 2304.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2304.1-h over \(\Q(\sqrt{3}) \)

Isogeny class 2304.1-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2304.1-h1	\( \bigl[0\) , \( a\) , \( 0\) , \( 22 a - 39\) , \( -95 a + 146\bigr] \)
2304.1-h2	\( \bigl[0\) , \( a\) , \( 0\) , \( -244 a + 420\) , \( -2504 a + 4336\bigr] \)
2304.1-h3	\( \bigl[0\) , \( a\) , \( 0\) , \( 86 a - 150\) , \( -440 a + 760\bigr] \)
2304.1-h4	\( \bigl[0\) , \( a\) , \( 0\) , \( 536 a - 960\) , \( 8488 a - 14792\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph