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

• Base field: \(\Q(\sqrt{30}) \)
• Label: 2.2.120.1-24.1-a
• 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-a over \(\Q(\sqrt{30}) \)

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

Curve label	Weierstrass Coefficients
24.1-a1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 690 a + 3786\) , \( -167310 a - 916398\bigr] \)
24.1-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a + 171\) , \( 315 a + 1722\bigr] \)
24.1-a3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -190 a - 1034\) , \( 2094 a + 11466\bigr] \)
24.1-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1070 a - 5854\) , \( -44886 a - 245854\bigr] \)
24.1-a5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2830 a - 15494\) , \( 185730 a + 1017282\bigr] \)
24.1-a6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -16910 a - 92614\) , \( -2837982 a - 15544270\bigr] \)

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