Elliptic curve isogeny class 1521.1-d over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.1-d
• Conductor: 1521.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1521.1-d over \(\Q(\sqrt{13}) \)

Isogeny class 1521.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1521.1-d1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1229 a + 2715\) , \( -1452 a + 3897\bigr] \)
1521.1-d2	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 273 a + 259\) , \( 12158 a + 15386\bigr] \)
1521.1-d3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 6 a - 15\) , \( 69 a - 159\bigr] \)
1521.1-d4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 201 a - 470\) , \( 2292 a - 5268\bigr] \)
1521.1-d5	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 266 a - 730\) , \( 329 a - 224\bigr] \)
1521.1-d6	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 2801 a - 8335\) , \( -127942 a + 326791\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph