Elliptic curve isogeny class 6.1-c over number field 3.3.1940.1

• Base field: 3.3.1940.1
• Label: 3.3.1940.1-6.1-c
• Conductor: 6.1
• Rank: \( 1 \)

Base field 3.3.1940.1

Generator \(a\), with minimal polynomial \( x^{3} - 8 x - 2 \); class number \(1\).

Elliptic curves in class 6.1-c over 3.3.1940.1

Isogeny class 6.1-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
6.1-c1	\( \bigl[a^{2} + a - 5\) , \( -a - 1\) , \( a + 1\) , \( -29 a^{2} - 65 a + 36\) , \( -278 a^{2} - 784 a - 95\bigr] \)
6.1-c2	\( \bigl[a^{2} + a - 5\) , \( a\) , \( a^{2} - 4\) , \( 461097919627 a^{2} - 116196853347 a - 3659501705210\) , \( 336783297466002456 a^{2} - 84869520681101411 a - 2672879227826975696\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph