Elliptic curve isogeny class with LMFDB label 327600.r (Cremona label 327600r)

• Label: 327600.r
• Number of curves: $1$
• Conductor: $327600$
• CM: no
• Rank: $1$

Rank

The elliptic curve 327600.r1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 327600.r do not have complex multiplication.

Modular form 327600.2.a.r

Elliptic curves in class 327600.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
327600.r1	327600r1	\([0, 0, 0, 31875, -2073125]\)	\(786080000/862407\)	\(-3929341893750000\)	\([]\)	\(1382400\)	\(1.6788\)	\(\Gamma_0(N)\)-optimal