Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1521.1-k
Conductor 1521.1
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 1521.1-k over \(\Q(\sqrt{13}) \)

Isogeny class 1521.1-k contains 4 curves linked by isogenies of degrees dividing 21.

Curve label Weierstrass Coefficients
1521.1-k1 \( \bigl[0\) , \( -1\) , \( 1\) , \( -26 a - 43\) , \( 65 a + 288\bigr] \)
1521.1-k2 \( \bigl[0\) , \( -1\) , \( 1\) , \( -2314 a - 2279\) , \( -67899 a - 97888\bigr] \)
1521.1-k3 \( \bigl[0\) , \( -1\) , \( 1\) , \( 26 a - 69\) , \( -65 a + 353\bigr] \)
1521.1-k4 \( \bigl[0\) , \( -1\) , \( 1\) , \( 2314 a - 4593\) , \( 67899 a - 165787\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph