Elliptic curve isogeny class with LMFDB label 27735.a (Cremona label 27735k)

• Label: 27735.a
• Number of curves: $1$
• Conductor: $27735$
• CM: no
• Rank: $1$

Rank

The elliptic curve 27735.a1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 27735.a do not have complex multiplication.

Modular form 27735.2.a.a

Elliptic curves in class 27735.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27735.a1	27735k1	\([0, 1, 1, -31026836, -67568222734]\)	\(-522547125460258816/9506987907075\)	\(-60097122063073750671675\)	\([]\)	\(4967424\)	\(3.1669\)	\(\Gamma_0(N)\)-optimal