Elliptic curve isogeny class 1521.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.1-b
• Conductor: 1521.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1521.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 1521.1-b contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
1521.1-b1	\( \bigl[0\) , \( -1\) , \( 1\) , \( 2 a - 5\) , \( 42 a - 97\bigr] \)
1521.1-b2	\( \bigl[0\) , \( -1\) , \( 1\) , \( -186 a + 375\) , \( -1854 a + 4439\bigr] \)
1521.1-b3	\( \bigl[0\) , \( -1\) , \( 1\) , \( -2 a - 3\) , \( -42 a - 55\bigr] \)
1521.1-b4	\( \bigl[0\) , \( -1\) , \( 1\) , \( 186 a + 189\) , \( 1854 a + 2585\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph