Elliptic curve isogeny class 23.2-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-23.2-a
• Conductor: 23.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 23.2-a over \(\Q(\sqrt{13}) \)

Isogeny class 23.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
23.2-a1	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a - 7\) , \( 10 a - 14\bigr] \)
23.2-a2	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 3\) , \( 2 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph