Elliptic curve isogeny class 75.2-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-75.2-a
• Conductor: 75.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 75.2-a over \(\Q(\sqrt{13}) \)

Isogeny class 75.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
75.2-a1	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 52 a - 125\) , \( -275 a + 631\bigr] \)
75.2-a2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 40 a + 51\) , \( 69 a + 89\bigr] \)
75.2-a3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -10 a - 14\) , \( -10 a - 14\bigr] \)
75.2-a4	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 2 a - 10\) , \( -3 a + 5\bigr] \)