Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-24.1-c
Conductor 24.1
Rank \( 1 \)

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Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 24.1-c over \(\Q(\sqrt{19}) \)

Isogeny class 24.1-c contains only one elliptic curve.

Curve label Weierstrass Coefficients
24.1-c1 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( -52701 a - 229718\) , \( 17439998 a + 76019186\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph