Elliptic curve isogeny class with LMFDB label 138675.q (Cremona label 138675u)

• Label: 138675.q
• Number of curves: $1$
• Conductor: $138675$
• CM: no
• Rank: $2$

Rank

The elliptic curve 138675.q1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 138675.q do not have complex multiplication.

Modular form 138675.2.a.q

Elliptic curves in class 138675.q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
138675.q1	138675u1	\([1, 1, 0, -12250, 465625]\)	\(7037694889/759375\)	\(21938818359375\)	\([]\)	\(403200\)	\(1.2940\)	\(\Gamma_0(N)\)-optimal