Elliptic curve isogeny class 45.1-c over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-45.1-c
• Conductor: 45.1
• Rank: \( 1 \)

Base field 4.4.4525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 3 x + 9 \); class number \(1\).

Elliptic curves in class 45.1-c over 4.4.4525.1

Isogeny class 45.1-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
45.1-c1	\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( a - 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 3\bigr] \)
45.1-c2	\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{7}{3} a\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( 3 a^{3} - 7 a^{2} + 12\) , \( -\frac{19}{3} a^{3} + \frac{73}{3} a^{2} + \frac{10}{3} a - 33\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph