Elliptic curve isogeny class 4.1-d over number field \(\Q(\sqrt{209}) \)

• Base field: \(\Q(\sqrt{209}) \)
• Label: 2.2.209.1-4.1-d
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-d over \(\Q(\sqrt{209}) \)

Isogeny class 4.1-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
4.1-d1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1485209680 a - 9993108793\) , \( 83988775088712 a + 565111430507277\bigr] \)
4.1-d2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 950 a + 6392\) , \( -42668 a - 287088\bigr] \)
4.1-d3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 1485209680 a - 11478318473\) , \( -83988775088712 a + 649100205595989\bigr] \)
4.1-d4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -950 a + 7342\) , \( 42668 a - 329756\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph