Elliptic curve isogeny class 108.1-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-108.1-a
• Conductor: 108.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 108.1-a over \(\Q(\sqrt{13}) \)

Isogeny class 108.1-a contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
108.1-a1	\( \bigl[a\) , \( a\) , \( a\) , \( 1707 a - 4095\) , \( 53306 a - 122129\bigr] \)
108.1-a2	\( \bigl[a\) , \( a\) , \( a\) , \( -18 a + 45\) , \( -19 a + 46\bigr] \)
108.1-a3	\( \bigl[a\) , \( a\) , \( a\) , \( 82 a - 195\) , \( -239 a + 538\bigr] \)
108.1-a4	\( \bigl[a\) , \( a\) , \( a\) , \( 1072 a - 2535\) , \( -26573 a + 61324\bigr] \)
108.1-a5	\( \bigl[a\) , \( a\) , \( a\) , \( 692 a - 1695\) , \( 13615 a - 31880\bigr] \)
108.1-a6	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -83860 a - 122846\) , \( 19206619 a + 24409255\bigr] \)
108.1-a7	\( \bigl[a\) , \( a\) , \( a\) , \( 27307 a - 65535\) , \( 3437626 a - 7866641\bigr] \)
108.1-a8	\( \bigl[a\) , \( a\) , \( a\) , \( 16267 a - 79935\) , \( 4343002 a - 6682673\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 10 & 20 & 20 & 4 & 2 & 4 \\ 5 & 1 & 2 & 4 & 4 & 20 & 10 & 20 \\ 10 & 2 & 1 & 2 & 2 & 10 & 5 & 10 \\ 20 & 4 & 2 & 1 & 4 & 20 & 10 & 5 \\ 20 & 4 & 2 & 4 & 1 & 5 & 10 & 20 \\ 4 & 20 & 10 & 20 & 5 & 1 & 2 & 4 \\ 2 & 10 & 5 & 10 & 10 & 2 & 1 & 2 \\ 4 & 20 & 10 & 5 & 20 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph