Properties

Base field \(\Q(\sqrt{85}) \)
Label 2.2.85.1-45.1-b
Conductor 45.1
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{85}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 21 \); class number \(2\).

Elliptic curves in class 45.1-b over \(\Q(\sqrt{85}) \)

Isogeny class 45.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
45.1-b1 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 1215 a - 6254\) , \( 92278 a - 472418\bigr] \)
45.1-b2 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 5 a + 16\) , \( -12 a + 142\bigr] \)
45.1-b3 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -380 a + 2011\) , \( 5119 a - 25982\bigr] \)
45.1-b4 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 115 a - 554\) , \( 538 a - 2708\bigr] \)
45.1-b5 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 60 a - 269\) , \( -521 a + 2728\bigr] \)
45.1-b6 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 1490 a - 7679\) , \( 66213 a - 339158\bigr] \)
45.1-b7 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 885 a - 4544\) , \( -31676 a + 161848\bigr] \)
45.1-b8 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 23765 a - 123104\) , \( 4305348 a - 22034198\bigr] \)

Rank

Rank not yet determined.

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