Elliptic curve isogeny class with Cremona label 15730o (LMFDB label 15730.a)

• Label: 15730o
• Number of curves: $1$
• Conductor: $15730$
• CM: no
• Rank: $1$

Rank

The elliptic curve 15730o1 has rank \(1\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 15730.2.a.o

Elliptic curves in class 15730o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15730.a1	15730o1	\([1, -1, 0, -369859, -176287787]\)	\(-3158470573163361/5758438400000\)	\(-10201424890342400000\)	\([]\)	\(748800\)	\(2.3375\)	\(\Gamma_0(N)\)-optimal