Elliptic curve isogeny class with Cremona label 1007a (LMFDB label 1007.a)

• Label: 1007a
• Number of curves: $1$
• Conductor: $1007$
• CM: no
• Rank: $1$

Rank

The elliptic curve 1007a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(19\)	\(1 + T\)
\(53\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1007a do not have complex multiplication.

Modular form 1007.2.a.a

Elliptic curves in class 1007a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1007.a1	1007a1	\([0, 0, 1, 61, -105]\)	\(25102282752/19266931\)	\(-19266931\)	\([]\)	\(276\)	\(0.085908\)	\(\Gamma_0(N)\)-optimal