Elliptic curve isogeny class 1764.3-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1764.3-b
• Conductor: 1764.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 1764.3-b over \(\Q(\sqrt{13}) \)

Isogeny class 1764.3-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
1764.3-b1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -7 a - 9\) , \( 12 a + 15\bigr] \)
1764.3-b2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 18 a + 26\) , \( -778 a - 1001\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph