Elliptic curve isogeny class 25344.2-i over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-25344.2-i
• Conductor: 25344.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 25344.2-i over \(\Q(\sqrt{-11}) \)

Isogeny class 25344.2-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
25344.2-i1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a + 28\) , \( -39 a + 36\bigr] \)
25344.2-i2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( 0\bigr] \)
25344.2-i3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -12\) , \( 12\bigr] \)
25344.2-i4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 33\) , \( 39 a - 3\bigr] \)

Rank

Rank: \( 1 \)

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