Elliptic curve isogeny class 20.1-a over number field \(\Q(\sqrt{30}) \)

• Base field: \(\Q(\sqrt{30}) \)
• Label: 2.2.120.1-20.1-a
• Conductor: 20.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 20.1-a over \(\Q(\sqrt{30}) \)

Isogeny class 20.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 404 a - 2180\) , \( -15305 a + 83885\bigr] \)
20.1-a2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -36 a + 230\) , \( 323 a - 1713\bigr] \)
20.1-a3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 234 a - 1275\) , \( 2643 a - 14473\bigr] \)
20.1-a4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 7274 a - 39835\) , \( -805965 a + 4414455\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph