Elliptic curve isogeny class 28.2-a over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-28.2-a
• Conductor: 28.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 23 \); class number \(1\).

Elliptic curves in class 28.2-a over \(\Q(\sqrt{23}) \)

Isogeny class 28.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
28.2-a1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 8 a + 12\) , \( 12 a + 40\bigr] \)
28.2-a2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 33 a - 108\) , \( 176 a - 747\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph