Elliptic curve isogeny class 26.1-d over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-26.1-d
• Conductor: 26.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 26.1-d over \(\Q(\sqrt{23}) \)

Isogeny class 26.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
26.1-d1	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 5 a + 16\) , \( 37 a + 174\bigr] \)
26.1-d2	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -55 a - 274\) , \( 307 a + 1466\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph