Elliptic curve isogeny class 171.1-e over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-171.1-e
• Conductor: 171.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 171.1-e over \(\Q(\sqrt{57}) \)

Isogeny class 171.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
171.1-e1	\( \bigl[1\) , \( a\) , \( 0\) , \( 1018 a + 3337\) , \( 104632 a + 342660\bigr] \)
171.1-e2	\( \bigl[1\) , \( a\) , \( 0\) , \( 6 a - 18\) , \( -18 a + 81\bigr] \)
171.1-e3	\( \bigl[1\) , \( a\) , \( 0\) , \( -182 a - 593\) , \( -2528 a - 8280\bigr] \)
171.1-e4	\( \bigl[1\) , \( a\) , \( 0\) , \( -782 a - 2558\) , \( 19744 a + 64659\bigr] \)
171.1-e5	\( \bigl[1\) , \( a\) , \( 0\) , \( -9960 a + 42585\) , \( -2264742 a + 9681588\bigr] \)
171.1-e6	\( \bigl[1\) , \( a\) , \( 0\) , \( -12182 a - 39893\) , \( 1403704 a + 4597014\bigr] \)

Rank

Rank: \( 0 \)

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