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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.1-j
• 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-j over \(\Q(\sqrt{13}) \)

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

Curve label	Weierstrass Coefficients
1521.1-j1	\( \bigl[1\) , \( a\) , \( 0\) , \( -6 a - 9\) , \( -69 a - 90\bigr] \)
1521.1-j2	\( \bigl[1\) , \( a\) , \( 0\) , \( 1229 a + 1486\) , \( 1452 a + 2445\bigr] \)
1521.1-j3	\( \bigl[1\) , \( a\) , \( 0\) , \( -266 a - 464\) , \( -329 a + 105\bigr] \)
1521.1-j4	\( \bigl[1\) , \( a\) , \( 0\) , \( -201 a - 269\) , \( -2292 a - 2976\bigr] \)
1521.1-j5	\( \bigl[1\) , \( a\) , \( 0\) , \( -2801 a - 5534\) , \( 127942 a + 198849\bigr] \)
1521.1-j6	\( \bigl[a\) , \( 1\) , \( 1\) , \( -274 a + 533\) , \( -12158 a + 27544\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph