Elliptic curve isogeny class 64.6-g over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-64.6-g
• Conductor: 64.6
• Rank: \( 1 \)

Base field \(\Q(\sqrt{209}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 52 \); class number \(1\).

Elliptic curves in class 64.6-g over \(\Q(\sqrt{209}) \)

Isogeny class 64.6-g contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
64.6-g1	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 310246949 a - 2397717530\) , \( -8088584565218 a + 62511947563426\bigr] \)
64.6-g2	\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 221320 a + 1489144\) , \( 8865401 a + 59650106\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph