Elliptic curve isogeny class 1300.1-g over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1300.1-g
• Conductor: 1300.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1300.1-g over \(\Q(\sqrt{13}) \)

Isogeny class 1300.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1300.1-g1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -67\) , \( -441\bigr] \)
1300.1-g2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -7\) , \( -1\bigr] \)
1300.1-g3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -87\) , \( -289\bigr] \)
1300.1-g4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1387\) , \( -19529\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph