Elliptic curve isogeny class 625.2-k over number field 3.3.169.1

• Base field: 3.3.169.1
• Label: 3.3.169.1-625.2-k
• Conductor: 625.2
• Rank: \( 0 \)

Base field 3.3.169.1

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 625.2-k over 3.3.169.1

Isogeny class 625.2-k contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
625.2-k1	\( \bigl[a^{2} - a - 3\) , \( 1\) , \( a^{2} - a - 3\) , \( 1797 a^{2} - 2413 a - 6738\) , \( -52408 a^{2} + 67787 a + 192749\bigr] \)
625.2-k2	\( \bigl[a^{2} - a - 3\) , \( 1\) , \( a^{2} - a - 3\) , \( 1837 a^{2} - 2348 a - 6718\) , \( -52853 a^{2} + 67342 a + 192989\bigr] \)
625.2-k3	\( \bigl[a^{2} - 2\) , \( a\) , \( a\) , \( 308 a^{2} - 389 a - 1121\) , \( 3789 a^{2} - 4826 a - 13832\bigr] \)
625.2-k4	\( \bigl[a^{2} - 2\) , \( a\) , \( a\) , \( 23 a^{2} - 24 a - 76\) , \( 54 a^{2} - 61 a - 187\bigr] \)