Properties

Base field \(\Q(\sqrt{23}) \)
Label 2.2.92.1-98.1-d
Conductor 98.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 23 \); class number \(1\).

Elliptic curves in class 98.1-d over \(\Q(\sqrt{23}) \)

Isogeny class 98.1-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
98.1-d1 \( \bigl[a\) , \( 1\) , \( a\) , \( -77610 a - 372201\) , \( 25832079 a + 123886304\bigr] \)
98.1-d2 \( \bigl[a\) , \( 1\) , \( a\) , \( -75 a - 356\) , \( 15363 a + 73684\bigr] \)
98.1-d3 \( \bigl[a\) , \( 1\) , \( a\) , \( 32730 a + 156969\) , \( -2454981 a - 11773676\bigr] \)
98.1-d4 \( \bigl[a\) , \( 1\) , \( a\) , \( -8745 a - 41936\) , \( -345713 a - 1657976\bigr] \)
98.1-d5 \( \bigl[a\) , \( 1\) , \( a\) , \( -4875 a - 23376\) , \( 391131 a + 1875804\bigr] \)
98.1-d6 \( \bigl[1\) , \( -1\) , \( 1\) , \( 77610 a - 372205\) , \( 25987299 a - 124630708\bigr] \)
98.1-d7 \( \bigl[1\) , \( -1\) , \( 1\) , \( 8745 a - 41940\) , \( -328223 a + 1574102\bigr] \)
98.1-d8 \( \bigl[1\) , \( -1\) , \( 1\) , \( -32730 a + 156965\) , \( -2520441 a + 12087612\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph