Properties

Base field 4.4.19796.1
Label 4.4.19796.1-10.2-d
Conductor 10.2
Rank \( 1 \)

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-d over 4.4.19796.1

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

Curve label Weierstrass Coefficients
10.2-d1 \( \bigl[a^{2} - a - 3\) , \( -a^{3} + 3 a^{2} + 3 a - 7\) , \( a^{3} - a^{2} - 5 a\) , \( -8 a^{3} + 19 a^{2} + 32 a - 58\) , \( 56 a^{3} - 136 a^{2} - 197 a + 316\bigr] \)
10.2-d2 \( \bigl[1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a\) , \( -97 a^{3} - 193 a^{2} + 110 a + 257\) , \( -2269 a^{3} - 4424 a^{2} + 2845 a + 6149\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph