Elliptic curve isogeny class 144.1-d over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-144.1-d
• Conductor: 144.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 144.1-d over \(\Q(\sqrt{22}) \)

Isogeny class 144.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
144.1-d1	\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 2\) , \( 10 a + 43\bigr] \)
144.1-d2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 27404 a - 128508\) , \( 5345218 a - 25071266\bigr] \)
144.1-d3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1789 a - 8363\) , \( 75880 a - 355880\bigr] \)
144.1-d4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 7894 a - 36998\) , \( -753290 a + 3533272\bigr] \)

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