Elliptic curve isogeny class 1369.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1369.1-c
• Conductor: 1369.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 1369.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 1369.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
1369.1-c1	\( \bigl[0\) , \( -1\) , \( a\) , \( -23\) , \( 49\bigr] \)
1369.1-c2	\( \bigl[0\) , \( -1\) , \( a\) , \( -3\) , \( -2\bigr] \)
1369.1-c3	\( \bigl[0\) , \( -1\) , \( a\) , \( -1873\) , \( 31832\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph