Elliptic curve isogeny class with Cremona label 2850z (LMFDB label 2850.bb)

• Label: 2850z
• Number of curves: $2$
• Conductor: $2850$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2850z have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2850z do not have complex multiplication.

Modular form 2850.2.a.z

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 2850z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2850.bb2	2850z1	\([1, 0, 0, -1963, -117583]\)	\(-53540005609/350208000\)	\(-5472000000000\)	\([2]\)	\(8064\)	\(1.1277\)	\(\Gamma_0(N)\)-optimal
2850.bb1	2850z2	\([1, 0, 0, -49963, -4293583]\)	\(882774443450089/2166000000\)	\(33843750000000\)	\([2]\)	\(16128\)	\(1.4742\)