Elliptic curve isogeny class 76.2-a over number field 4.4.16225.1

• Base field: 4.4.16225.1
• Label: 4.4.16225.1-76.2-a
• Number of curves: 1
• Conductor: 76.2
• Rank: \( 0 \)

Base field 4.4.16225.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 13 x^{2} + 6 x + 36 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 76.2-a over 4.4.16225.1

Isogeny class 76.2-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
76.2-a1	\( \bigl[\frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{1}{6} a\) , \( -\frac{1}{6} a^{3} + \frac{7}{6} a^{2} - \frac{5}{6} a - 8\) , \( \frac{1}{6} a^{3} + \frac{5}{6} a^{2} - \frac{13}{6} a - 6\) , \( \frac{3419}{2} a^{3} + \frac{3989}{2} a^{2} - \frac{35883}{2} a - 28533\) , \( -\frac{420308}{3} a^{3} - \frac{487420}{3} a^{2} + \frac{4411274}{3} a + 2335211\bigr] \)