Properties

Base field 4.4.13824.1
Label 4.4.13824.1-6.1-d
Conductor 6.1
Rank \( 0 \)

Related objects

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Base field 4.4.13824.1

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

Elliptic curves in class 6.1-d over 4.4.13824.1

Isogeny class 6.1-d contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
6.1-d1 \( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -19 a^{3} + 10 a^{2} + 80 a - 67\) , \( 68 a^{3} - 106 a^{2} - 351 a + 437\bigr] \)
6.1-d2 \( \bigl[a^{2} - 3\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 3\) , \( -763 a^{3} + 2310 a^{2} + 280 a - 3691\) , \( 27132 a^{3} - 49741 a^{2} - 44144 a + 52109\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph