Elliptic curve isogeny class 14400.6-k over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.6-k
• Conductor: 14400.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 14400.6-k over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.6-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14400.6-k1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -27 a + 67\) , \( 75 a + 216\bigr] \)
14400.6-k2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 33 a + 47\) , \( -13 a + 812\bigr] \)
14400.6-k3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 153 a - 993\) , \( -3285 a + 10836\bigr] \)
14400.6-k4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 873 a + 767\) , \( -3973 a + 32132\bigr] \)

Rank

Rank: \( 0 \)

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