Properties

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

Related objects

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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-d over 6.6.1241125.1

Isogeny class 25.2-d contains only one elliptic curve.

Curve label Weierstrass Coefficients
25.2-d1 \( \bigl[a^{2} + a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -8 a^{5} + 3 a^{4} + 53 a^{3} - 5 a^{2} - 79 a - 22\) , \( -8 a^{5} + 3 a^{4} + 54 a^{3} - 4 a^{2} - 83 a - 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph