Elliptic curve isogeny class 1521.2-i over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1521.2-i
• Conductor: 1521.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 1521.2-i over \(\Q(\sqrt{13}) \)

Isogeny class 1521.2-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1521.2-i1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 352 a - 36\) , \( 6262 a + 4339\bigr] \)
1521.2-i2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -103 a - 231\) , \( 776 a + 1336\bigr] \)
1521.2-i3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -38 a - 36\) , \( -160 a - 185\bigr] \)
1521.2-i4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1598 a - 3546\) , \( 58314 a + 98017\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph