Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-56.1-a
Conductor 56.1
Rank not recorded

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 56.1-a over \(\Q(\sqrt{7}) \)

Isogeny class 56.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
56.1-a1 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 14 a + 36\) , \( 221 a + 584\bigr] \)
56.1-a2 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -706 a - 1869\) , \( -14839 a - 39261\bigr] \)
56.1-a3 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -226 a - 599\) , \( 2341 a + 6193\bigr] \)
56.1-a4 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3586 a - 9489\) , \( 181961 a + 481423\bigr] \)

Rank

Rank not yet determined.

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