Properties

Base field 4.4.19796.1
Label 4.4.19796.1-10.2-e
Conductor 10.2
Rank \( 0 \)

Related objects

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Base field 4.4.19796.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + x + 8 \); class number \(1\).

Elliptic curves in class 10.2-e over 4.4.19796.1

Isogeny class 10.2-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
10.2-e1 \( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 8\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -33 a^{3} - 27 a^{2} + 66 a + 10\) , \( 222 a^{3} + 633 a^{2} - 148 a - 1028\bigr] \)
10.2-e2 \( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( 3 a^{3} - 23 a - 23\) , \( -16 a^{3} - 2 a^{2} + 107 a + 105\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph