Elliptic curve isogeny class 39600.5-b over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-39600.5-b
• Conductor: 39600.5
• Rank: \( 2 \)

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

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

Elliptic curves in class 39600.5-b over \(\Q(\sqrt{-11}) \)

Isogeny class 39600.5-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
39600.5-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 10\bigr] \)
39600.5-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 35 a + 9\) , \( 7 a + 177\bigr] \)
39600.5-b3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -35 a + 44\) , \( -7 a + 184\bigr] \)
39600.5-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -76\) , \( 280\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph