Elliptic curve isogeny class with Cremona label 388416f (LMFDB label 388416.f)

• Label: 388416f
• Number of curves: $1$
• Conductor: $388416$
• CM: no
• Rank: $1$

Rank

The elliptic curve 388416f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 388416f do not have complex multiplication.

Modular form 388416.2.a.f

Elliptic curves in class 388416f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388416.f1	388416f1	\([0, -1, 0, 33532863, -31952231199]\)	\(2280364702703/1560674304\)	\(-2853931683441671160201216\)	\([]\)	\(79902720\)	\(3.3812\)	\(\Gamma_0(N)\)-optimal