Elliptic curve isogeny class 121.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-121.1-b
• Conductor: 121.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 121.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 121.1-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
121.1-b1	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 437938 a - 758571\) , \( -207226626 a + 358927153\bigr] \)
121.1-b2	\( \bigl[0\) , \( 1\) , \( a\) , \( -10\) , \( 19\bigr] \)
121.1-b3	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 18 a - 31\) , \( 154 a - 267\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph