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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-39600.5-a
• Conductor: 39600.5
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
39600.5-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 85 a - 36\) , \( -327 a - 336\bigr] \)
39600.5-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -85 a + 49\) , \( 327 a - 663\bigr] \)
39600.5-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -21\) , \( -54\bigr] \)
39600.5-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -396\) , \( -2904\bigr] \)

Rank

Rank: \( 1 \)

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