Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-15876.2-c
Conductor 15876.2
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 15876.2-c over \(\Q(\sqrt{-7}) \)

Isogeny class 15876.2-c contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
15876.2-c1 \( \bigl[1\) , \( -1\) , \( 0\) , \( 21 a - 93\) , \( -91 a + 377\bigr] \)
15876.2-c2 \( \bigl[1\) , \( -1\) , \( 0\) , \( -21 a - 72\) , \( 91 a + 286\bigr] \)
15876.2-c3 \( \bigl[1\) , \( -1\) , \( 0\) , \( 39 a + 24\) , \( 13 a + 38\bigr] \)
15876.2-c4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -39 a + 63\) , \( -13 a + 51\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph