Elliptic curve isogeny class 4.2-a over number field 4.4.19025.1

• Base field: 4.4.19025.1
• Label: 4.4.19025.1-4.2-a
• Conductor: 4.2
• Rank: \( 1 \)

Base field 4.4.19025.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 13 x^{2} + 14 x + 44 \); class number \(1\).

Elliptic curves in class 4.2-a over 4.4.19025.1

Isogeny class 4.2-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
4.2-a1	\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( -23 a^{3} - 16 a^{2} + 250 a + 364\) , \( \frac{29}{2} a^{3} + 10 a^{2} - \frac{319}{2} a - 232\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph