Elliptic curve isogeny class with Cremona label 126350cu (LMFDB label 126350.dh)

• Label: 126350cu
• Number of curves: $4$
• Conductor: $126350$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 126350cu have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 126350cu do not have complex multiplication.

Modular form 126350.2.a.cu

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 126350cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126350.dh4	126350cu1	\([1, -1, 1, 20870, 1843497]\)	\(1367631/2800\)	\(-2058257293750000\)	\([2]\)	\(691200\)	\(1.6228\)	\(\Gamma_0(N)\)-optimal
126350.dh3	126350cu2	\([1, -1, 1, -159630, 19893497]\)	\(611960049/122500\)	\(90048756601562500\)	\([2, 2]\)	\(1382400\)	\(1.9694\)
126350.dh2	126350cu3	\([1, -1, 1, -791380, -253022503]\)	\(74565301329/5468750\)	\(4020033776855468750\)	\([2]\)	\(2764800\)	\(2.3159\)
126350.dh1	126350cu4	\([1, -1, 1, -2415880, 1445843497]\)	\(2121328796049/120050\)	\(88247781469531250\)	\([2]\)	\(2764800\)	\(2.3159\)