Elliptic curve isogeny class with Cremona label 67335j (LMFDB label 67335.k)

• Label: 67335j
• Number of curves: $1$
• Conductor: $67335$
• CM: no
• Rank: $1$

Rank

The elliptic curve 67335j1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(67\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - 2 T + 2 T^{2}\)	1.2.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 67335j do not have complex multiplication.

Modular form 67335.2.a.j

Elliptic curves in class 67335j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
67335.k1	67335j1	\([0, 1, 1, -151083280, 754282037809]\)	\(-14018440572928/922640625\)	\(-25101853899481567584421875\)	\([]\)	\(22962240\)	\(3.6262\)	\(\Gamma_0(N)\)-optimal