Elliptic curve isogeny class 15.2-e over number field \(\Q(\sqrt{69}) \)

• Base field: \(\Q(\sqrt{69}) \)
• Label: 2.2.69.1-15.2-e
• Conductor: 15.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{69}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 17 \); class number \(1\).

Elliptic curves in class 15.2-e over \(\Q(\sqrt{69}) \)

Isogeny class 15.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
15.2-e1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 32\) , \( 32 a - 96\bigr] \)
15.2-e2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 175 a - 783\) , \( -2383 a + 11139\bigr] \)
15.2-e3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 45 a - 178\) , \( 221 a - 978\bigr] \)
15.2-e4	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 635 a - 2933\) , \( 17021 a - 79203\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph