Elliptic curve isogeny class with LMFDB label 84700.z (Cremona label 84700h)

• Label: 84700.z
• Number of curves: $1$
• Conductor: $84700$
• CM: no
• Rank: $1$

Rank

The elliptic curve 84700.z1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 84700.z do not have complex multiplication.

Modular form 84700.2.a.z

Elliptic curves in class 84700.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
84700.z1	84700h1	\([0, 1, 0, -64533, -6996937]\)	\(-4194304/539\)	\(-3819485516000000\)	\([]\)	\(403200\)	\(1.7235\)	\(\Gamma_0(N)\)-optimal