Elliptic curve isogeny class 1521.3-i over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.3-i
• Conductor: 1521.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 1521.3-i over \(\Q(\sqrt{13}) \)

Isogeny class 1521.3-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1521.3-i1	\( \bigl[a\) , \( -a\) , \( 0\) , \( 38 a - 74\) , \( 160 a - 345\bigr] \)
1521.3-i2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 103 a - 334\) , \( -776 a + 2112\bigr] \)
1521.3-i3	\( \bigl[a\) , \( -a\) , \( 0\) , \( -352 a + 316\) , \( -6262 a + 10601\bigr] \)
1521.3-i4	\( \bigl[a\) , \( -a\) , \( 0\) , \( 1598 a - 5144\) , \( -58314 a + 156331\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph