Properties

Base field 4.4.13824.1
Label 4.4.13824.1-12.1-c
Conductor 12.1
Rank \( 1 \)

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 12.1-c over 4.4.13824.1

Isogeny class 12.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
12.1-c1 \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a\) , \( 55 a^{3} + 20 a^{2} - 217 a - 191\) , \( 217 a^{3} + 453 a^{2} - 1246 a - 1668\bigr] \)
12.1-c2 \( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( -13 a^{3} + 4 a^{2} + 46 a - 39\) , \( -8 a^{3} + 36 a^{2} + 69 a - 112\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph