Properties

Base field 6.6.485125.1
Label 6.6.485125.1-49.1-g
Conductor 49.1
Rank \( 1 \)

Related objects

Learn more

Base field 6.6.485125.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 8 x^{3} + 2 x^{2} - 5 x + 1 \); class number \(1\).

Elliptic curves in class 49.1-g over 6.6.485125.1

Isogeny class 49.1-g contains only one elliptic curve.

Curve label Weierstrass Coefficients
49.1-g1 \( \bigl[a + 1\) , \( -2 a^{5} + 2 a^{4} + 10 a^{3} - 7 a^{2} - 9 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 2\) , \( -2 a^{5} + 2 a^{4} + 8 a^{3} - 4 a^{2} - 7 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 2 a^{2} + 6 a + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph