Properties

Base field 3.3.940.1
Label 3.3.940.1-16.4-d
Conductor 16.4
Rank not recorded

Related objects

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Base field 3.3.940.1

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

Elliptic curves in class 16.4-d over 3.3.940.1

Isogeny class 16.4-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
16.4-d1 \( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a^{2} - 4\) , \( 9453243 a^{2} - 5697518 a - 62738784\) , \( 27206223747 a^{2} - 16397325199 a - 180560817484\bigr] \)
16.4-d2 \( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a^{2} - 4\) , \( 590913 a^{2} - 356148 a - 3921744\) , \( 425398375 a^{2} - 256389699 a - 2823261292\bigr] \)
16.4-d3 \( \bigl[a\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 4\) , \( 776001989 a^{2} - 467700226 a - 5150128688\) , \( 37939505091840 a^{2} - 22866326787280 a - 251794887741124\bigr] \)
16.4-d4 \( \bigl[a\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - a - 4\) , \( 27 a^{2} - 17 a - 175\) , \( 104 a^{2} - 55 a - 676\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph