Elliptic curve isogeny class 4.1-c over number field 4.4.17600.1

• Base field: 4.4.17600.1
• Label: 4.4.17600.1-4.1-c
• Conductor: 4.1
• Rank: \( 0 \)

Base field 4.4.17600.1

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

Elliptic curves in class 4.1-c over 4.4.17600.1

Isogeny class 4.1-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4.1-c1	\( \bigl[\frac{1}{2} a^{3} - 4 a + 1\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 4\) , \( 2 a^{3} + 3 a^{2} - 18 a - 27\) , \( \frac{461}{2} a^{3} + \frac{1003}{2} a^{2} - 2129 a - 4637\bigr] \)
4.1-c2	\( \bigl[\frac{1}{2} a^{3} - 4 a + 1\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 4\) , \( -23 a^{3} - 57 a^{2} + 182 a + 433\) , \( -\frac{12443}{2} a^{3} - \frac{27249}{2} a^{2} + 57233 a + 125135\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph