Properties

Base field 4.4.13768.1
Label 4.4.13768.1-6.1-c
Conductor 6.1
Rank \( 0 \)

Related objects

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Base field 4.4.13768.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} + 2 x + 2 \); class number \(1\).

Elliptic curves in class 6.1-c over 4.4.13768.1

Isogeny class 6.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
6.1-c1 \( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -160 a^{3} + 239 a^{2} + 685 a - 654\) , \( 1542 a^{3} - 2291 a^{2} - 6590 a + 6286\bigr] \)
6.1-c2 \( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 4\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -30 a^{3} + 44 a^{2} + 130 a - 114\) , \( -169 a^{3} + 251 a^{2} + 724 a - 686\bigr] \)
6.1-c3 \( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 4 a - 1\) , \( a^{2} - 2\) , \( 4 a^{3} - a^{2} - 17 a - 6\) , \( 6 a^{3} - a^{2} - 29 a - 14\bigr] \)
6.1-c4 \( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 0\) , \( 17 a^{3} - 3 a^{2} - 87 a - 35\) , \( 61 a^{3} - 10 a^{2} - 312 a - 141\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph