Elliptic curve isogeny class 121.1-a over number field \(\Q(\sqrt{15}) \)

• Base field: \(\Q(\sqrt{15}) \)
• Label: 2.2.60.1-121.1-a
• Conductor: 121.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{15}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 15 \); class number \(2\).

Elliptic curves in class 121.1-a over \(\Q(\sqrt{15}) \)

Isogeny class 121.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
121.1-a1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 250250 a - 969716\) , \( -134564648 a + 521170522\bigr] \)
121.1-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 330 a - 1276\) , \( -12208 a + 47282\bigr] \)
121.1-a3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a - 36\) , \( 72 a - 278\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph