Elliptic curve isogeny class 15.1-c over number field 5.5.157457.1

• Base field: 5.5.157457.1
• Label: 5.5.157457.1-15.1-c
• Conductor: 15.1
• Rank: \( 1 \)

Base field 5.5.157457.1

Generator \(a\), with minimal polynomial \( x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 4 x - 1 \); class number \(1\).

Elliptic curves in class 15.1-c over 5.5.157457.1

Isogeny class 15.1-c contains only one elliptic curve.

Curve label	Weierstrass Coefficients
15.1-c1	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( -a^{4} + 3 a^{3} + a^{2} - 6 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -4 a^{4} + 10 a^{3} + 9 a^{2} - 24 a + 2\) , \( -6 a^{4} + 17 a^{3} + 10 a^{2} - 38 a + 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph