Elliptic curve isogeny class with LMFDB label 78650.be (Cremona label 78650n)

• Label: 78650.be
• Number of curves: $1$
• Conductor: $78650$
• CM: no
• Rank: $1$

Rank

The elliptic curve 78650.be1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 78650.be do not have complex multiplication.

Modular form 78650.2.a.be

Elliptic curves in class 78650.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78650.be1	78650n1	\([1, 0, 1, -406926, -97858752]\)	\(2224882033/53248\)	\(178346588992000000\)	\([]\)	\(811008\)	\(2.0950\)	\(\Gamma_0(N)\)-optimal