Elliptic curve isogeny class with LMFDB label 121275.w (Cremona label 121275bs)

• Label: 121275.w
• Number of curves: $1$
• Conductor: $121275$
• CM: no
• Rank: $1$

Rank

The elliptic curve 121275.w1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 121275.w do not have complex multiplication.

Modular form 121275.2.a.w

Elliptic curves in class 121275.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121275.w1	121275bs1	\([0, 0, 1, -5530875, 5006460156]\)	\(61549867008/1331\)	\(404628229564453125\)	\([]\)	\(5483520\)	\(2.4950\)	\(\Gamma_0(N)\)-optimal