Elliptic curve isogeny class 40.1-c over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-40.1-c
• Conductor: 40.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 40.1-c over \(\Q(\sqrt{15}) \)

Isogeny class 40.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
40.1-c1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -24 a + 107\) , \( 295 a - 1123\bigr] \)
40.1-c2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 16 a - 48\) , \( 37 a - 124\bigr] \)
40.1-c3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 64 a - 248\) , \( -504 a + 1952\bigr] \)
40.1-c4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 216 a - 823\) , \( 3157 a - 12209\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph