Elliptic curve isogeny class with LMFDB label 27225.be (Cremona label 27225r)

• Label: 27225.be
• Number of curves: $2$
• Conductor: $27225$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Rank

The elliptic curves in class 27225.be have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 + 17 T^{2}\)	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 27225.be has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 27225.2.a.be

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 27225.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
27225.be1	27225r2	\([0, 0, 1, 0, -2470669]\)	\(0\)	\(-2637016159201875\)	\([]\)	\(180576\)	\(1.6379\)		\(-3\)
27225.be2	27225r1	\([0, 0, 1, 0, 91506]\)	\(0\)	\(-3617306116875\)	\([3]\)	\(60192\)	\(1.0886\)	\(\Gamma_0(N)\)-optimal	\(-3\)