Elliptic curve isogeny class 144.5-c over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.5-c
• Conductor: 144.5
• Rank: \( 1 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 144.5-c over \(\Q(\sqrt{57}) \)

Isogeny class 144.5-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
144.5-c1	\( \bigl[a\) , \( a\) , \( 0\) , \( 157 a + 514\) , \( 136994 a + 448644\bigr] \)
144.5-c2	\( \bigl[a\) , \( a\) , \( 0\) , \( 866 a - 3676\) , \( -26773 a + 114478\bigr] \)
144.5-c3	\( \bigl[a\) , \( a\) , \( 0\) , \( 3 a + 6\) , \( 0\bigr] \)
144.5-c4	\( \bigl[a\) , \( a\) , \( 0\) , \( -1208 a - 3956\) , \( 40103 a + 131334\bigr] \)
144.5-c5	\( \bigl[a\) , \( a\) , \( 0\) , \( -12 a - 24\) , \( -87 a - 294\bigr] \)
144.5-c6	\( \bigl[a\) , \( a\) , \( 0\) , \( 4929 a - 21045\) , \( 949077 a - 4057200\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph