Elliptic curve isogeny class with Cremona label 50700c (LMFDB label 50700.f)

• Label: 50700c
• Number of curves: $2$
• Conductor: $50700$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 50700c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 50700c do not have complex multiplication.

Modular form 50700.2.a.c

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 50700c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
50700.f2	50700c1	\([0, -1, 0, -2253, -59463]\)	\(-40960/27\)	\(-834072595200\)	\([]\)	\(73872\)	\(0.98839\)	\(\Gamma_0(N)\)-optimal
50700.f1	50700c2	\([0, -1, 0, -205053, -35671143]\)	\(-30866268160/3\)	\(-92674732800\)	\([]\)	\(221616\)	\(1.5377\)