Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-468.1-e
Conductor 468.1
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 468.1-e over \(\Q(\sqrt{13}) \)

Isogeny class 468.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
468.1-e1 \( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 685\bigr] \)
468.1-e2 \( \bigl[1\) , \( 1\) , \( 0\) , \( 10760 a - 16039\) , \( 528536 a - 1327919\bigr] \)
468.1-e3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -2339\) , \( -15747\bigr] \)
468.1-e4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -1299\) , \( 17325\bigr] \)
468.1-e5 \( \bigl[1\) , \( 1\) , \( 0\) , \( -10760 a - 5279\) , \( -528536 a - 799383\bigr] \)
468.1-e6 \( \bigl[1\) , \( 1\) , \( 0\) , \( -20739\) , \( 1140957\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph