Properties

Base field 4.4.16997.1
Label 4.4.16997.1-5.2-b
Conductor 5.2
Rank \( 1 \)

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 5.2-b over 4.4.16997.1

Isogeny class 5.2-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
5.2-b1 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -5 a^{3} - 12 a^{2} + a + 10\) , \( -30 a^{3} - 71 a^{2} + 13 a + 63\bigr] \)
5.2-b2 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 3\) , \( a\) , \( -1147 a^{3} + 1237 a^{2} + 5259 a - 4929\) , \( -37920 a^{3} + 42325 a^{2} + 176448 a - 163829\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph