Elliptic curve isogeny class 20.1-d over number field \(\Q(\sqrt{301}) \)

• Base field: \(\Q(\sqrt{301}) \)
• Label: 2.2.301.1-20.1-d
• Conductor: 20.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{301}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 75 \); class number \(1\).

Elliptic curves in class 20.1-d over \(\Q(\sqrt{301}) \)

Isogeny class 20.1-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
20.1-d1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -68 a - 530\) , \( -6625 a - 54095\bigr] \)
20.1-d2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -10 a + 105\) , \( -31 a + 343\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph