Elliptic curve isogeny class with Cremona label 225318x (LMFDB label 225318.i)

• Label: 225318x
• Number of curves: $1$
• Conductor: $225318$
• CM: no
• Rank: $2$

Rank

The elliptic curve 225318x1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(17\)	\(1 + T\)
\(47\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 225318x do not have complex multiplication.

Modular form 225318.2.a.x

Elliptic curves in class 225318x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
225318.i1	225318x1	\([1, 0, 1, -1386, 19792]\)	\(-133157973625/446148\)	\(-985540932\)	\([]\)	\(135168\)	\(0.59032\)	\(\Gamma_0(N)\)-optimal