Elliptic curve isogeny class 90.1-b over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-90.1-b
• Conductor: 90.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 90.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 90.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
90.1-b1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -8\) , \( 11\bigr] \)
90.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 188 a + 727\) , \( -191 a - 743\bigr] \)
90.1-b3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -772 a - 2993\) , \( -8303 a - 32159\bigr] \)
90.1-b4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -128\) , \( 587\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph