Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-324.2-d
Conductor 324.2
Rank \( 1 \)

Related objects

Learn more

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 324.2-d over \(\Q(\sqrt{13}) \)

Isogeny class 324.2-d contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
324.2-d1 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -9 a - 5\) , \( 25 a + 28\bigr] \)
324.2-d2 \( \bigl[a\) , \( a\) , \( 1\) , \( -a - 3\) , \( a + 4\bigr] \)