Elliptic curve isogeny class 576.2-g over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-576.2-g
• Conductor: 576.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 576.2-g over \(\Q(\sqrt{13}) \)

Isogeny class 576.2-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.2-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 9\) , \( 32 a + 26\bigr] \)
576.2-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 6\) , \( 4 a + 5\bigr] \)
576.2-g3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -29 a - 36\) , \( -108 a - 142\bigr] \)
576.2-g4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -59 a - 81\) , \( 340 a + 446\bigr] \)

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