Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-98.1-b
Conductor 98.1
Rank not recorded

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Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 98.1-b over \(\Q(\sqrt{19}) \)

Isogeny class 98.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
98.1-b1 \( \bigl[a\) , \( 1\) , \( a\) , \( -169\) , \( 535\bigr] \)
98.1-b2 \( \bigl[a\) , \( 1\) , \( a\) , \( 1\) , \( 1\bigr] \)
98.1-b3 \( \bigl[a\) , \( 1\) , \( a\) , \( 6\) , \( 17\bigr] \)
98.1-b4 \( \bigl[a\) , \( 1\) , \( a\) , \( -34\) , \( 1\bigr] \)
98.1-b5 \( \bigl[a\) , \( 1\) , \( a\) , \( -9\) , \( -31\bigr] \)
98.1-b6 \( \bigl[a\) , \( 1\) , \( a\) , \( -2729\) , \( 49687\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph