Elliptic curve isogeny class 676.1-d over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-676.1-d
• Conductor: 676.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 676.1-d over \(\Q(\sqrt{13}) \)

Isogeny class 676.1-d contains 6 curves linked by isogenies of degrees dividing 45.

Curve label	Weierstrass Coefficients
676.1-d1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -1540 a + 3469\) , \( -25760 a + 59481\bigr] \)
676.1-d2	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( a - 8\) , \( -13 a + 16\bigr] \)
676.1-d3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -322\) , \( 2127\bigr] \)
676.1-d4	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -a - 7\) , \( 14 a + 10\bigr] \)
676.1-d5	\( \bigl[1\) , \( 1\) , \( 1\) , \( 3\) , \( -5\bigr] \)
676.1-d6	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1540 a + 1930\) , \( 24220 a + 31792\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 45 & 3 & 5 & 15 & 9 \\ 45 & 1 & 15 & 9 & 3 & 5 \\ 3 & 15 & 1 & 15 & 5 & 3 \\ 5 & 9 & 15 & 1 & 3 & 45 \\ 15 & 3 & 5 & 3 & 1 & 15 \\ 9 & 5 & 3 & 45 & 15 & 1 \end{array}\right)\)

Isogeny graph