Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-2500.2-b
Conductor 2500.2
Rank \( 1 \)

Related objects

Learn more about

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

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

Elliptic curves in class 2500.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 2500.2-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
2500.2-b1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \)
2500.2-b2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
2500.2-b3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( -219\bigr] \)
2500.2-b4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph