Elliptic curve isogeny class 1764.2-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1764.2-b
• Conductor: 1764.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1764.2-b over \(\Q(\sqrt{13}) \)

Isogeny class 1764.2-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
1764.2-b1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 6 a - 15\) , \( -12 a + 27\bigr] \)
1764.2-b2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -19 a + 45\) , \( 778 a - 1779\bigr] \)