Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-12.1-a
Conductor 12.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 12.1-a over \(\Q(\sqrt{10}) \)

Isogeny class 12.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
12.1-a1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a - 42\) , \( 390 a + 1238\bigr] \)
12.1-a2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 7\) , \( -3 a - 12\bigr] \)
12.1-a3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -34 a - 102\) , \( 162 a + 510\bigr] \)
12.1-a4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -534 a - 1682\) , \( 11534 a + 36470\bigr] \)

Rank

Rank: \( 0 \)

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