Elliptic curve isogeny class 36.1-b over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-36.1-b
• Conductor: 36.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 36.1-b over \(\Q(\sqrt{15}) \)

Isogeny class 36.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -504 a - 1952\bigr] \)
36.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 30744 a + 119071\bigr] \)
36.1-b3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -27 a - 102\) , \( -258 a - 1000\bigr] \)
36.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -7440 a - 28815\) , \( 676368 a + 2619562\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph