Elliptic curve isogeny class with LMFDB label 1512.d (Cremona label 1512k)

• Label: 1512.d
• Number of curves: $1$
• Conductor: $1512$
• CM: no
• Rank: $1$

Rank

The elliptic curve 1512.d1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1512.d do not have complex multiplication.

Modular form 1512.2.a.d

Elliptic curves in class 1512.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1512.d1	1512k1	\([0, 0, 0, -108, 324]\)	\(27648/7\)	\(35271936\)	\([]\)	\(288\)	\(0.15796\)	\(\Gamma_0(N)\)-optimal