Elliptic curve isogeny class with LMFDB label 309680.bt (Cremona label 309680bt)

• Label: 309680.bt
• Number of curves: $1$
• Conductor: $309680$
• CM: no
• Rank: $1$

Rank

The elliptic curve 309680.bt1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 309680.bt do not have complex multiplication.

Modular form 309680.2.a.bt

Elliptic curves in class 309680.bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
309680.bt1	309680bt1	\([0, 0, 0, -121843547, 549350206986]\)	\(-172898395855742529/12621798400000\)	\(-14603655765474515353600000\)	\([]\)	\(66044160\)	\(3.5779\)	\(\Gamma_0(N)\)-optimal