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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2401.1-a
• Conductor: 2401.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
2401.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
2401.1-a2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 6002 a - 10397\) , \( -408170 a + 706971\bigr] \)
2401.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
2401.1-a4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 102042 a - 176752\) , \( -23325715 a + 40401332\bigr] \)

Rank

Rank: \( 0 \)

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