Elliptic curve isogeny class with LMFDB label 309738.y (Cremona label 309738y)

• Label: 309738.y
• Number of curves: $1$
• Conductor: $309738$
• CM: no
• Rank: $1$

Rank

The elliptic curve 309738.y1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 309738.y do not have complex multiplication.

Modular form 309738.2.a.y

Elliptic curves in class 309738.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
309738.y1	309738y1	\([1, 0, 1, -16614, -868040]\)	\(-10779215329/658944\)	\(-31000601009664\)	\([]\)	\(1026432\)	\(1.3434\)	\(\Gamma_0(N)\)-optimal