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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2304.1-z
• Conductor: 2304.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
2304.1-z1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 134 a - 231\) , \( 1031 a - 1786\bigr] \)
2304.1-z2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 18\) , \( -16 a + 28\bigr] \)
2304.1-z3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 160 a - 288\) , \( -1396 a + 2440\bigr] \)
2304.1-z4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a + 12\) , \( -124 a + 184\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph