Properties

Base field 4.4.12725.1
Label 4.4.12725.1-11.3-d
Conductor 11.3
Rank \( 1 \)

Related objects

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Base field 4.4.12725.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 10 x^{2} + 11 x + 29 \); class number \(1\).

Elliptic curves in class 11.3-d over 4.4.12725.1

Isogeny class 11.3-d contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
11.3-d1 \( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 6\) , \( a^{2} - a - 5\) , \( -3 a^{3} - 3 a^{2} + 24 a + 36\) , \( a^{3} - 10 a - 12\bigr] \)
11.3-d2 \( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 6\) , \( a^{2} - a - 5\) , \( -58 a^{3} - 53 a^{2} + 359 a + 436\) , \( -641 a^{3} - 660 a^{2} + 4121 a + 5573\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph