Elliptic curve isogeny class 169.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-169.1-b
• Conductor: 169.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 169.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 169.1-b contains 4 curves linked by isogenies of degrees dividing 57.

Curve label	Weierstrass Coefficients
169.1-b1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 1727 a - 5907\) , \( -68712 a + 192070\bigr] \)
169.1-b2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -1727 a - 4177\) , \( 66984 a + 119182\bigr] \)
169.1-b3	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -2 a - 2\) , \( -6 a - 8\bigr] \)
169.1-b4	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 7\) , \( 3 a - 10\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 57 & 19 \\ 3 & 1 & 19 & 57 \\ 57 & 19 & 1 & 3 \\ 19 & 57 & 3 & 1 \end{array}\right)\)

Isogeny graph