Elliptic curve isogeny class with LMFDB label 234135.w (Cremona label 234135w)

• Label: 234135.w
• Number of curves: $1$
• Conductor: $234135$
• CM: no
• Rank: $1$

Rank

The elliptic curve 234135.w1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 234135.w do not have complex multiplication.

Modular form 234135.2.a.w

Elliptic curves in class 234135.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
234135.w1	234135w1	\([0, 0, 1, -1782, 9875]\)	\(262766592/134375\)	\(320033278125\)	\([]\)	\(172800\)	\(0.89994\)	\(\Gamma_0(N)\)-optimal