Elliptic curve isogeny class 1764.1-n over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1764.1-n
• Conductor: 1764.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1764.1-n over \(\Q(\sqrt{13}) \)

Isogeny class 1764.1-n contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
1764.1-n1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2718 a - 6345\) , \( -104850 a + 241660\bigr] \)
1764.1-n2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5607 a + 13080\) , \( -542259 a + 1250362\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph