Properties

Base field 3.3.1396.1
Label 3.3.1396.1-20.3-a
Conductor 20.3
Rank \( 0 \)

Related objects

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Base field 3.3.1396.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 5 \); class number \(1\).

Elliptic curves in class 20.3-a over 3.3.1396.1

Isogeny class 20.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
20.3-a1 \( \bigl[a^{2} - 5\) , \( a - 1\) , \( 0\) , \( -3 a^{2} - 4 a + 12\) , \( -9 a^{2} - 15 a + 19\bigr] \)
20.3-a2 \( \bigl[a^{2} - 5\) , \( a - 1\) , \( 0\) , \( -203 a^{2} - 374 a + 362\) , \( -4073 a^{2} - 7507 a + 7163\bigr] \)
20.3-a3 \( \bigl[a + 1\) , \( a^{2} - 6\) , \( a^{2} - 5\) , \( 4209 a^{2} + 7762 a - 7392\) , \( -1506114 a^{2} - 2776380 a + 2648427\bigr] \)
20.3-a4 \( \bigl[a + 1\) , \( a^{2} - 6\) , \( a^{2} - 5\) , \( -337566 a^{2} - 622268 a + 593603\) , \( -257569576 a^{2} - 474804914 a + 452924609\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph