Elliptic curve isogeny class 100.1-c over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-100.1-c
• Conductor: 100.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{85}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 21 \); class number \(2\).

Elliptic curves in class 100.1-c over \(\Q(\sqrt{85}) \)

Isogeny class 100.1-c contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
100.1-c1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
100.1-c2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 38 a - 155\) , \( -295 a + 1579\bigr] \)
100.1-c3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
100.1-c4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -237 a + 1270\) , \( 2250 a - 11351\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph