Elliptic curve isogeny class 3675.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3675.1-b
• Conductor: 3675.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 3675.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 3675.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3675.1-b1	\( \bigl[a\) , \( -1\) , \( a\) , \( 16\) , \( 36\bigr] \)
3675.1-b2	\( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( 6\bigr] \)
3675.1-b3	\( \bigl[a\) , \( -1\) , \( a\) , \( -4\) , \( -2\bigr] \)
3675.1-b4	\( \bigl[a\) , \( -1\) , \( a\) , \( -114\) , \( 468\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph