Elliptic curve isogeny class 900.3-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-900.3-b
• Conductor: 900.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 900.3-b over \(\Q(\sqrt{13}) \)

Isogeny class 900.3-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
900.3-b1	\( \bigl[a\) , \( -1\) , \( a\) , \( -13 a - 19\) , \( 19 a + 24\bigr] \)
900.3-b2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -4 a + 12\) , \( 643 a - 1480\bigr] \)