Elliptic curve isogeny class 5.1-b over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-5.1-b
• Conductor: 5.1
• Rank: \( 0 \)

Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 5.1-b over 6.6.1241125.1

Isogeny class 5.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
5.1-b1	\( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( 4 a^{5} - a^{4} - 28 a^{3} - a^{2} + 44 a + 15\) , \( a^{2} + a - 2\) , \( 27 a^{5} - 5 a^{4} - 189 a^{3} - 19 a^{2} + 305 a + 129\) , \( 54 a^{5} - 13 a^{4} - 375 a^{3} - 21 a^{2} + 598 a + 243\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph