Elliptic curve isogeny class 1521.2-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.2-a
• Conductor: 1521.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1521.2-a over \(\Q(\sqrt{13}) \)

Isogeny class 1521.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1521.2-a1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 42 a - 239\) , \( -480 a + 1252\bigr] \)
1521.2-a2	\( \bigl[a\) , \( a\) , \( 1\) , \( -50 a - 60\) , \( 180 a + 226\bigr] \)
1521.2-a3	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -23 a - 44\) , \( -90 a - 74\bigr] \)
1521.2-a4	\( \bigl[a\) , \( a\) , \( 1\) , \( -765 a - 1035\) , \( 14896 a + 19336\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph