Properties

Base field 4.4.5125.1
Label 4.4.5125.1-41.1-e
Conductor 41.1
Rank \( 1 \)

Related objects

Learn more

Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 41.1-e over 4.4.5125.1

Isogeny class 41.1-e contains only one elliptic curve.

Curve label Weierstrass Coefficients
41.1-e1 \( \bigl[0\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( 6 a^{3} - 20 a^{2} - 3 a + 39\) , \( -9 a^{3} + 32 a^{2} - 5 a - 48\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph