Elliptic curve isogeny class 3.1-a over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-3.1-a
• Conductor: 3.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3.1-a over \(\Q(\sqrt{22}) \)

Isogeny class 3.1-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
3.1-a1	\( \bigl[1\) , \( -a\) , \( 1\) , \( -5 a - 16\) , \( 19 a + 93\bigr] \)
3.1-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 1657 a + 7782\) , \( -67542 a - 316799\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph