Properties

Base field \(\Q(\sqrt{38}) \)
Label 2.2.152.1-19.1-e
Conductor 19.1
Rank \( 1 \)

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Base field \(\Q(\sqrt{38}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 38 \); class number \(1\).

Elliptic curves in class 19.1-e over \(\Q(\sqrt{38}) \)

Isogeny class 19.1-e contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
19.1-e1 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 341584 a - 2105665\) , \( -269922166 a + 1663911967\bigr] \)
19.1-e2 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 4144 a - 25545\) , \( -384936 a + 2372892\bigr] \)
19.1-e3 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 296 a + 1825\) , \( 205 a + 1257\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph