Elliptic curve isogeny class 625.1-e over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-625.1-e
• Conductor: 625.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 625.1-e over \(\Q(\sqrt{13}) \)

Isogeny class 625.1-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
625.1-e1	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 6 a - 11\) , \( -5 a + 13\bigr] \)
625.1-e2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 81 a - 186\) , \( -505 a + 1163\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph