Properties

Base field 6.6.1241125.1
Label 6.6.1241125.1-25.2-a
Conductor 25.2
Rank \( 1 \)

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Base field 6.6.1241125.1

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

Elliptic curves in class 25.2-a over 6.6.1241125.1

Isogeny class 25.2-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
25.2-a1 \( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 2 a^{2} + 20 a + 5\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 19\) , \( -6 a^{5} + 2 a^{4} + 40 a^{3} - 60 a - 21\) , \( -5 a^{5} + a^{4} + 35 a^{3} + 3 a^{2} - 55 a - 24\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph