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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.3-g
• Conductor: 1521.3
• Rank: \( 0 \)

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

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

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

Isogeny class 1521.3-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1521.3-g1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 142 a - 343\) , \( -1266 a + 2985\bigr] \)
1521.3-g2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 12 a - 18\) , \( 21 a - 44\bigr] \)
1521.3-g3	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 142 a - 343\) , \( 1282 a - 3021\bigr] \)
1521.3-g4	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 77 a - 668\) , \( 983 a + 1243\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph