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

• Label: 27225ba
• Number of curves: $2$
• Conductor: $27225$
• CM: \(\Q(\sqrt{-11}) \)
• Rank: $0$

Rank

The elliptic curves in class 27225ba have rank \(0\).

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
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 27225ba has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).

Modular form 27225.2.a.ba

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 27225ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
27225.ba2	27225ba1	\([0, 0, 1, -1650, -26469]\)	\(-32768\)	\(-15160921875\)	\([]\)	\(12960\)	\(0.73095\)	\(\Gamma_0(N)\)-optimal	\(-11\)
27225.ba1	27225ba2	\([0, 0, 1, -199650, 35229906]\)	\(-32768\)	\(-26858497917796875\)	\([]\)	\(142560\)	\(1.9299\)		\(-11\)