Elliptic curve isogeny class with Cremona label 177840dz (LMFDB label 177840.bp)

• Label: 177840dz
• Number of curves: $1$
• Conductor: $177840$
• CM: no
• Rank: $1$

Rank

The elliptic curve 177840dz1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 177840dz do not have complex multiplication.

Modular form 177840.2.a.dz

Elliptic curves in class 177840dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177840.bp1	177840dz1	\([0, 0, 0, -678506943, 6802672688633]\)	\(-2961686524287311350789156096/139506818115234375\)	\(-1627207526496093750000\)	\([]\)	\(39075840\)	\(3.5483\)	\(\Gamma_0(N)\)-optimal