Elliptic curve isogeny class with LMFDB label 216225.y (Cremona label 216225bk)

• Label: 216225.y
• Number of curves: $2$
• Conductor: $216225$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Rank

The elliptic curves in class 216225.y have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 216225.y has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 216225.2.a.y

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 216225.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
216225.y1	216225bk1	\([0, 0, 1, 0, -178932194]\)	\(0\)	\(-13831227342801016875\)	\([]\)	\(2432880\)	\(2.3517\)	\(\Gamma_0(N)\)-optimal	\(-3\)
216225.y2	216225bk2	\([0, 0, 1, 0, 4831169231]\)	\(0\)	\(-10082964732901941301875\)	\([]\)	\(7298640\)	\(2.9010\)		\(-3\)