Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-576.2-c
Conductor 576.2
Rank \( 1 \)

Related objects

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 576.2-c over \(\Q(\sqrt{7}) \)

Isogeny class 576.2-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
576.2-c1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 1\) , \( -7 a + 17\bigr] \)
576.2-c2 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -51 a - 135\) , \( 271 a + 717\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph