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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.2-g
• 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-g over \(\Q(\sqrt{13}) \)

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

Curve label	Weierstrass Coefficients
1521.2-g1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -75 a - 594\) , \( -1577 a + 2594\bigr] \)
1521.2-g2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -10 a - 9\) , \( -30 a - 45\bigr] \)
1521.2-g3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -140 a - 204\) , \( 1062 a + 1502\bigr] \)
1521.2-g4	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -140 a - 204\) , \( -1486 a - 1956\bigr] \)

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