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

• Label: 27225.i
• Number of curves: $1$
• Conductor: $27225$
• CM: no
• Rank: $0$

Rank

The elliptic curve 27225.i1 has 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 \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 27225.i do not have complex multiplication.

Modular form 27225.2.a.i

Elliptic curves in class 27225.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27225.i1	27225bd1	\([1, -1, 1, -1310, -21018]\)	\(-10241915/2187\)	\(-53051097825\)	\([]\)	\(16128\)	\(0.77917\)	\(\Gamma_0(N)\)-optimal