Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-225.1-a
Conductor 225.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{21}) \)

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

Elliptic curves in class 225.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 225.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
225.1-a1 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 334 a - 983\) , \( 9901 a - 27378\bigr] \)
225.1-a2 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4 a + 7\) , \( a + 12\bigr] \)
225.1-a3 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -101 a + 322\) , \( 547 a - 1437\bigr] \)
225.1-a4 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 34 a - 83\) , \( 61 a - 168\bigr] \)
225.1-a5 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 19 a - 38\) , \( -53 a + 153\bigr] \)
225.1-a6 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 409 a - 1208\) , \( 7111 a - 19743\bigr] \)
225.1-a7 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 244 a - 713\) , \( -3383 a + 9198\bigr] \)
225.1-a8 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 6484 a - 19433\) , \( 461521 a - 1272408\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph