Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-56.1-c
Conductor 56.1
Rank \( 0 \)

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-c over \(\Q(\sqrt{7}) \)

Isogeny class 56.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
56.1-c1 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -2 a - 4\) , \( -396 a - 1048\bigr] \)
56.1-c2 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 485 a - 1278\) , \( 8998 a - 23802\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph