Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-1156.3-b
Conductor 1156.3
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 1156.3-b over \(\Q(\sqrt{13}) \)

Isogeny class 1156.3-b contains 6 curves linked by isogenies of degrees dividing 45.

Curve label Weierstrass Coefficients
1156.3-b1 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -784 a - 740\) , \( 12288 a + 16948\bigr] \)
1156.3-b2 \( \bigl[1\) , \( a\) , \( 1\) , \( 16 a - 37\) , \( -159 a + 364\bigr] \)
1156.3-b3 \( \bigl[a\) , \( 1\) , \( 1\) , \( 520 a - 1287\) , \( -9127 a + 21283\bigr] \)
1156.3-b4 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 11 a - 25\) , \( 23 a - 50\bigr] \)
1156.3-b5 \( \bigl[a\) , \( 1\) , \( 1\) , \( -5 a + 13\) , \( 23 a - 53\bigr] \)
1156.3-b6 \( \bigl[a + 1\) , \( a\) , \( a\) , \( 556 a + 258\) , \( 3332 a + 8420\bigr] \)

Rank

Rank: \( 0 \)

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