Properties

Base field 4.4.9792.1
Label 4.4.9792.1-36.1-d
Conductor 36.1
Rank \( 1 \)

Related objects

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Base field 4.4.9792.1

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

Elliptic curves in class 36.1-d over 4.4.9792.1

Isogeny class 36.1-d contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
36.1-d1 \( \bigl[1\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( 0\) , \( -1420 a^{3} + 1299 a^{2} + 11345 a + 9299\) , \( -199304 a^{3} + 185398 a^{2} + 1593168 a + 1304734\bigr] \)
36.1-d2 \( \bigl[a + 1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( -2 a^{3} + 5 a^{2} + 8 a - 7\) , \( a^{3} - 11 a^{2} - 6 a + 16\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph