Properties

Base field 4.4.8768.1
Label 4.4.8768.1-7.4-a
Conductor 7.4
Rank \( 0 \)

Related objects

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Base field 4.4.8768.1

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

Elliptic curves in class 7.4-a over 4.4.8768.1

Isogeny class 7.4-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
7.4-a1 \( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -9 a^{3} - 4 a^{2} + 30 a + 17\) , \( 28 a^{3} + 18 a^{2} - 90 a - 74\bigr] \)
7.4-a2 \( \bigl[a^{3} - a^{2} - 3 a\) , \( a - 1\) , \( a^{2} - 2\) , \( -32 a^{3} - 23 a^{2} + 105 a + 92\) , \( 189 a^{3} + 127 a^{2} - 614 a - 505\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph