Elliptic curve isogeny class 2401.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2401.1-b
• Conductor: 2401.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 2401.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 2401.1-b contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
2401.1-b1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
2401.1-b2	\( \bigl[1\) , \( -1\) , \( a\) , \( 6002 a - 10397\) , \( 408170 a - 706972\bigr] \)
2401.1-b3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -37\) , \( 78\bigr] \)
2401.1-b4	\( \bigl[1\) , \( -1\) , \( a\) , \( 102042 a - 176752\) , \( 23325715 a - 40401333\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph