Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-256.1-d
Conductor 256.1
Rank \( 1 \)

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 256.1-d over \(\Q(\sqrt{13}) \)

Isogeny class 256.1-d contains 6 curves linked by isogenies of degrees dividing 45.

Curve label Weierstrass Coefficients
256.1-d1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1894 a + 4271\) , \( 34785 a - 79853\bigr] \)
256.1-d2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 9\) , \( 9 a - 37\bigr] \)
256.1-d3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 395\) , \( 1581 a - 988\bigr] \)
256.1-d4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8\) , \( 8 a + 20\bigr] \)
256.1-d5 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -3 a + 4\bigr] \)
256.1-d6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1896 a + 2376\) , \( 36680 a + 47444\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 45 & 3 & 5 & 15 & 9 \\ 45 & 1 & 15 & 9 & 3 & 5 \\ 3 & 15 & 1 & 15 & 5 & 3 \\ 5 & 9 & 15 & 1 & 3 & 45 \\ 15 & 3 & 5 & 3 & 1 & 15 \\ 9 & 5 & 3 & 45 & 15 & 1 \end{array}\right)\)

Isogeny graph