Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-19881.1-b
Conductor 19881.1
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 19881.1-b over \(\Q(\sqrt{-7}) \)

Isogeny class 19881.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
19881.1-b1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -2\) , \( 3\bigr] \)
19881.1-b2 \( \bigl[1\) , \( 0\) , \( 0\) , \( -62\) , \( 33\bigr] \)
19881.1-b3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -47\) , \( 120\bigr] \)
19881.1-b4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -752\) , \( 7875\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph