Elliptic curve isogeny class 19.1-b over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-19.1-b
• Conductor: 19.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 19.1-b over \(\Q(\sqrt{57}) \)

Isogeny class 19.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
19.1-b1	\( \bigl[0\) , \( a\) , \( 1\) , \( 9293547 a - 39729138\) , \( -29973404577 a + 128133823300\bigr] \)
19.1-b2	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -112747 a - 369231\) , \( 42718257 a + 139898758\bigr] \)
19.1-b3	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 8053 a + 26379\) , \( 24987 a + 81833\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph