Elliptic curve isogeny class with Cremona label 5070s (LMFDB label 5070.r)

• Label: 5070s
• Number of curves: $1$
• Conductor: $5070$
• CM: no
• Rank: $1$

Rank

The elliptic curve 5070s1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5070s do not have complex multiplication.

Modular form 5070.2.a.s

Elliptic curves in class 5070s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5070.r1	5070s1	\([1, 1, 1, -16260, 799365]\)	\(-2813198004118489/33177600000\)	\(-5607014400000\)	\([]\)	\(16320\)	\(1.2588\)	\(\Gamma_0(N)\)-optimal