LMFDB - Elliptic curve isogeny class 19.1-a over number field 4.4.19525.1

Base field 4.4.19525.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 14 x^{2} + 15 x + 45 \); class number \(1\).

Isogeny class 19.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 3 a\) , \( a\) , \( -6 a^{3} + \frac{50}{3} a^{2} + \frac{163}{3} a - 119\) , \( 23 a^{3} - \frac{260}{3} a^{2} - \frac{559}{3} a + 685\bigr] \)
19.1-a2	\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 3 a\) , \( a\) , \( -a^{3} - \frac{5}{3} a^{2} + \frac{38}{3} a + 26\) , \( \frac{1}{3} a^{3} - 5 a^{2} + \frac{2}{3} a + 48\bigr] \)

Rank: \( 1 \)

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

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