Properties

Base field 4.4.16997.1
Label 4.4.16997.1-7.1-a
Conductor 7.1
Rank \( 0 \)

Related objects

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Base field 4.4.16997.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - x + 5 \); class number \(1\).

Elliptic curves in class 7.1-a over 4.4.16997.1

Isogeny class 7.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
7.1-a1 \( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{2} - 3\) , \( 2 a^{3} - 6 a^{2} - 16 a + 12\) , \( -a^{3} - 9 a^{2} - 8 a + 13\bigr] \)
7.1-a2 \( \bigl[a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -59 a^{3} - 68 a^{2} + 316 a + 398\) , \( 750 a^{3} + 650 a^{2} - 3904 a - 4142\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph