Elliptic curve isogeny class 128.5-c over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-128.5-c
• Conductor: 128.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 128.5-c over \(\Q(\sqrt{57}) \)

Isogeny class 128.5-c contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
128.5-c1	\( \bigl[a\) , \( a\) , \( a\) , \( 115785 a - 497049\) , \( 41797219 a - 178648906\bigr] \)
128.5-c2	\( \bigl[a\) , \( -1\) , \( a\) , \( -2811454 a - 9207370\) , \( 4982304576 a + 16316634679\bigr] \)
128.5-c3	\( \bigl[a\) , \( a\) , \( a\) , \( -345 a + 1491\) , \( -6165 a + 26374\bigr] \)
128.5-c4	\( \bigl[a\) , \( -1\) , \( a\) , \( 8426 a + 27590\) , \( -733568 a - 2402377\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph