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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-675.1-h
• Conductor: 675.1
• Rank: \( 0 \)

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

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

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

Isogeny class 675.1-h contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
675.1-h1	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 4 a - 27\) , \( -38 a + 14\bigr] \)
675.1-h2	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -6 a - 12\) , \( -8 a - 13\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph