Elliptic curve isogeny class 12.1-c over number field 4.4.18097.1

• Base field: 4.4.18097.1
• Label: 4.4.18097.1-12.1-c
• Conductor: 12.1
• Rank: \( 1 \)

Base field 4.4.18097.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 6 x + 4 \); class number \(1\).

Elliptic curves in class 12.1-c over 4.4.18097.1

Isogeny class 12.1-c contains only one elliptic curve.

Curve label	Weierstrass Coefficients
12.1-c1	\( \bigl[a^{3} - 5 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( -\frac{3}{2} a^{3} + \frac{3}{2} a^{2} + \frac{13}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph