Elliptic curve isogeny class 11.1-a over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-11.1-a
• Conductor: 11.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{22}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 22 \); class number \(1\).

Elliptic curves in class 11.1-a over \(\Q(\sqrt{22}) \)

Isogeny class 11.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
11.1-a1	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -129410876 a - 606990812\) , \( 1735544452344 a + 8140425051145\bigr] \)
11.1-a2	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -170996 a - 802042\) , \( 151040284 a + 708441725\bigr] \)
11.1-a3	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -5516 a - 25872\) , \( -1145176 a - 5371355\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph