Properties

Base field 6.6.300125.1
Label 6.6.300125.1-49.1-a
Conductor 49.1
Rank \( 0 \)

Related objects

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Base field 6.6.300125.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 49.1-a over 6.6.300125.1

Isogeny class 49.1-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
49.1-a1 \( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 120 a^{5} - 30 a^{4} - 870 a^{3} - 390 a^{2} + 570 a + 91\) , \( 408 a^{5} - 102 a^{4} - 2958 a^{3} - 1326 a^{2} + 1938 a + 324\bigr] \)
49.1-a2 \( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph