Elliptic curve isogeny class with LMFDB label 194040.n (Cremona label 194040ff)

• Label: 194040.n
• Number of curves: $1$
• Conductor: $194040$
• CM: no
• Rank: $2$

Rank

The elliptic curve 194040.n1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 194040.n do not have complex multiplication.

Modular form 194040.2.a.n

Elliptic curves in class 194040.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
194040.n1	194040ff1	\([0, 0, 0, 252, -28]\)	\(5225472/3025\)	\(-1024531200\)	\([]\)	\(82944\)	\(0.41842\)	\(\Gamma_0(N)\)-optimal