Elliptic curve isogeny class 24.1-c over number field \(\Q(\sqrt{30}) \)

• Base field: \(\Q(\sqrt{30}) \)
• Label: 2.2.120.1-24.1-c
• Conductor: 24.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{30}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 30 \); class number \(2\).

Elliptic curves in class 24.1-c over \(\Q(\sqrt{30}) \)

Isogeny class 24.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
24.1-c1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -178 a + 978\) , \( -21912 a + 120018\bigr] \)
24.1-c2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -118 a + 653\) , \( 1749 a - 9583\bigr] \)
24.1-c3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 42 a - 227\) , \( 526 a - 2880\bigr] \)
24.1-c4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 262 a - 1432\) , \( -4084 a + 22370\bigr] \)
24.1-c5	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 702 a - 3842\) , \( 27268 a - 149352\bigr] \)
24.1-c6	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 4222 a - 23122\) , \( -330496 a + 1810202\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph