Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-37125.7-k
Conductor 37125.7
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 37125.7-k over \(\Q(\sqrt{-11}) \)

Isogeny class 37125.7-k contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
37125.7-k1 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 10555 a - 34319\) , \( -1072600 a + 2175843\bigr] \)
37125.7-k2 \( \bigl[a\) , \( 0\) , \( 1\) , \( 11 a + 669\) , \( -4019 a + 2152\bigr] \)
37125.7-k3 \( \bigl[a\) , \( 0\) , \( 1\) , \( 3806 a + 3279\) , \( 40681 a - 300248\bigr] \)
37125.7-k4 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 655 a - 2144\) , \( -17755 a + 33978\bigr] \)
37125.7-k5 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 70 a - 74\) , \( -169 a + 1191\bigr] \)
37125.7-k6 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 115 a - 3089\) , \( -32794 a - 10059\bigr] \)
37125.7-k7 \( \bigl[a\) , \( 0\) , \( 1\) , \( 146 a + 624\) , \( -3893 a - 2690\bigr] \)
37125.7-k8 \( \bigl[a\) , \( 0\) , \( 1\) , \( -1354 a - 2751\) , \( -39143 a - 13940\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 12 & 2 & 4 & 4 & 6 & 3 \\ 12 & 1 & 4 & 6 & 3 & 12 & 2 & 4 \\ 12 & 4 & 1 & 6 & 12 & 3 & 2 & 4 \\ 2 & 6 & 6 & 1 & 2 & 2 & 3 & 6 \\ 4 & 3 & 12 & 2 & 1 & 4 & 6 & 12 \\ 4 & 12 & 3 & 2 & 4 & 1 & 6 & 12 \\ 6 & 2 & 2 & 3 & 6 & 6 & 1 & 2 \\ 3 & 4 & 4 & 6 & 12 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph