Properties

Base field 4.4.17609.1
Label 4.4.17609.1-20.1-b
Conductor 20.1
Rank \( 1 \)

Related objects

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Base field 4.4.17609.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 10 x - 1 \); class number \(1\).

Elliptic curves in class 20.1-b over 4.4.17609.1

Isogeny class 20.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
20.1-b1 \( \bigl[a^{3} - 6 a + 3\) , \( a^{3} - 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -53 a^{3} + 45 a^{2} + 376 a - 488\) , \( -630 a^{3} + 514 a^{2} + 4622 a - 5937\bigr] \)
20.1-b2 \( \bigl[a^{3} - 6 a + 3\) , \( a^{3} - 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 7 a^{3} - 5 a^{2} - 49 a + 57\) , \( 15 a^{3} - 12 a^{2} - 113 a + 143\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph