Elliptic curve isogeny class 30.1-l over number field \(\Q(\sqrt{30}) \)

• Base field: \(\Q(\sqrt{30}) \)
• Label: 2.2.120.1-30.1-l
• Conductor: 30.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 30.1-l over \(\Q(\sqrt{30}) \)

Isogeny class 30.1-l contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
30.1-l1	\( \bigl[a\) , \( 1\) , \( a\) , \( -45\) , \( 363\bigr] \)
30.1-l2	\( \bigl[a\) , \( 1\) , \( a\) , \( 15\) , \( 15\bigr] \)
30.1-l3	\( \bigl[a\) , \( 1\) , \( a\) , \( -1805\) , \( -1077\bigr] \)
30.1-l4	\( \bigl[a\) , \( 1\) , \( a\) , \( -265\) , \( 743\bigr] \)
30.1-l5	\( \bigl[a\) , \( 1\) , \( a\) , \( -65\) , \( -417\bigr] \)
30.1-l6	\( \bigl[a\) , \( 1\) , \( a\) , \( -1325\) , \( 14955\bigr] \)
30.1-l7	\( \bigl[a\) , \( 1\) , \( a\) , \( -1145\) , \( -18345\bigr] \)
30.1-l8	\( \bigl[a\) , \( 1\) , \( a\) , \( -21325\) , \( 1138955\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph