Elliptic curve isogeny class 900.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-900.1-b
• Conductor: 900.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 900.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 900.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
900.1-b1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -16 a - 24\) , \( -76 a + 302\bigr] \)
900.1-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -56 a - 111\) , \( 287 a + 511\bigr] \)
900.1-b3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -a - 54\) , \( -4 a + 152\bigr] \)
900.1-b4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -226 a - 504\) , \( 2966 a + 4922\bigr] \)

Rank

Rank: \( 0 \)

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