Elliptic curve isogeny class 25.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-25.1-a
• Conductor: 25.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 25.1-a over \(\Q(\sqrt{11}) \)

Isogeny class 25.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -2 a - 10\) , \( -4 a - 16\bigr] \)
25.1-a2	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 126 a - 425\) , \( -1231 a + 4080\bigr] \)
25.1-a3	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( a - 10\) , \( 4 a - 16\bigr] \)
25.1-a4	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -127 a - 425\) , \( 1231 a + 4080\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph