Elliptic curve isogeny class with LMFDB label 15730.d (Cremona label 15730c)

• Label: 15730.d
• Number of curves: $1$
• Conductor: $15730$
• CM: no
• Rank: $2$

Rank

The elliptic curve 15730.d1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 15730.d do not have complex multiplication.

Modular form 15730.2.a.d

Elliptic curves in class 15730.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15730.d1	15730c1	\([1, 1, 0, -13, -7]\)	\(2259169/1300\)	\(157300\)	\([]\)	\(1920\)	\(-0.31325\)	\(\Gamma_0(N)\)-optimal