Elliptic curve isogeny class with Cremona label 104742j (LMFDB label 104742.u)

• Label: 104742j
• Number of curves: $1$
• Conductor: $104742$
• CM: no
• Rank: $1$

Rank

The elliptic curve 104742j1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 104742j do not have complex multiplication.

Modular form 104742.2.a.j

Elliptic curves in class 104742j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
104742.u1	104742j1	\([1, -1, 0, -15161414121, 720121383516109]\)	\(-3571480626044740843224673/9021299988885921792\)	\(-973562123403214395454067761152\)	\([]\)	\(230630400\)	\(4.6313\)	\(\Gamma_0(N)\)-optimal