Elliptic curve isogeny class 3136.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3136.1-c
• Conductor: 3136.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3136.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 3136.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3136.1-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 60 a - 104\) , \( 474 a - 820\bigr] \)
3136.1-c2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 1045 a - 1811\) , \( 23911 a - 41415\bigr] \)
3136.1-c3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -64\) , \( 138 a\bigr] \)
3136.1-c4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 64 a - 133\) , \( 303 a - 501\bigr] \)

Rank

Rank: \( 1 \)

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