Properties

Base field 4.4.11525.1
Label 4.4.11525.1-11.1-c
Conductor 11.1
Rank bounds 0...1

Related objects

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Base field 4.4.11525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 5 x + 25 \); class number \(1\).

Elliptic curves in class 11.1-c over 4.4.11525.1

Isogeny class 11.1-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
11.1-c1 \( \bigl[\frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{1}{5} a\) , \( -\frac{1}{5} a^{3} + \frac{1}{5} a^{2} + \frac{11}{5} a\) , \( \frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{6}{5} a + 1\) , \( -\frac{61}{5} a^{3} + \frac{231}{5} a^{2} + \frac{111}{5} a - 124\) , \( -\frac{68}{5} a^{3} + \frac{193}{5} a^{2} + \frac{148}{5} a - 102\bigr] \)
11.1-c2 \( \bigl[a\) , \( a^{2} - a - 7\) , \( a^{2} - a - 5\) , \( -\frac{761}{5} a^{3} - \frac{1469}{5} a^{2} + \frac{3836}{5} a + 1340\) , \( -\frac{16893}{5} a^{3} - \frac{35292}{5} a^{2} + \frac{74938}{5} a + 27840\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph