Elliptic curve isogeny class 14400.4-j over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-14400.4-j
• Conductor: 14400.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 14400.4-j over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.4-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14400.4-j1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 834 a + 519\) , \( 2433 a - 27597\bigr] \)
14400.4-j2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a - 201\) , \( 105 a - 2445\bigr] \)
14400.4-j3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 54 a + 39\) , \( 45 a - 405\bigr] \)
14400.4-j4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a + 24\) , \( -17 a + 78\bigr] \)

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