Elliptic curve isogeny class with LMFDB label 119850.u (Cremona label 119850ba)

• Label: 119850.u
• Number of curves: $2$
• Conductor: $119850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 119850.u have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(17\)	\(1 - T\)
\(47\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 119850.u do not have complex multiplication.

Modular form 119850.2.a.u

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 119850.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
119850.u1	119850ba2	\([1, 0, 1, -407801, 37810748]\)	\(480006385101608833/238183351674336\)	\(3721614869911500000\)	\([2]\)	\(2457600\)	\(2.2564\)
119850.u2	119850ba1	\([1, 0, 1, -219801, -39269252]\)	\(75160530649878913/900176053248\)	\(14065250832000000\)	\([2]\)	\(1228800\)	\(1.9098\)	\(\Gamma_0(N)\)-optimal