Elliptic curve isogeny class 49005.6-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-49005.6-b
• Conductor: 49005.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 49005.6-b over \(\Q(\sqrt{-11}) \)

Isogeny class 49005.6-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
49005.6-b1	\( \bigl[1\) , \( -1\) , \( a\) , \( 181 a + 27\) , \( -388 a - 2009\bigr] \)
49005.6-b2	\( \bigl[1\) , \( -1\) , \( a\) , \( -974 a + 522\) , \( 2307 a - 15935\bigr] \)
49005.6-b3	\( \bigl[1\) , \( -1\) , \( a\) , \( 16 a + 27\) , \( -58 a + 70\bigr] \)
49005.6-b4	\( \bigl[1\) , \( -1\) , \( a\) , \( -479 a + 27\) , \( -4920 a + 5845\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph