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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-900.3-a
• 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-a over \(\Q(\sqrt{13}) \)

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

Curve label	Weierstrass Coefficients
900.3-a1	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 107 a - 235\) , \( 771 a - 1772\bigr] \)
900.3-a2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 7 a - 15\) , \( 11 a - 28\bigr] \)