Elliptic curve isogeny class 675.4-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-675.4-b
• Conductor: 675.4
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

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

Elliptic curves in class 675.4-b over \(\Q(\sqrt{-11}) \)

Isogeny class 675.4-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
675.4-b1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 49\) , \( -94 a - 2\bigr] \)
675.4-b2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2 a + 4\) , \( -2 a - 5\bigr] \)
675.4-b3	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 72 a - 251\) , \( -477 a + 645\bigr] \)
675.4-b4	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 17 a - 131\) , \( 134 a - 504\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph