Elliptic curve isogeny class 675.1-g over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-675.1-g
• Conductor: 675.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 675.1-g over \(\Q(\sqrt{13}) \)

Isogeny class 675.1-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
675.1-g1	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 83 a - 219\) , \( -684 a + 1625\bigr] \)
675.1-g2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 82 a - 177\) , \( 282 a - 639\bigr] \)
675.1-g3	\( \bigl[a\) , \( 0\) , \( a\) , \( -53 a - 72\) , \( -53 a - 71\bigr] \)
675.1-g4	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -2 a - 24\) , \( a + 44\bigr] \)

Rank

Rank: \( 1 \)

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