Elliptic curve isogeny class with Cremona label 19950ce (LMFDB label 19950.cn)

• Label: 19950ce
• Number of curves: $4$
• Conductor: $19950$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 19950ce have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 19950ce do not have complex multiplication.

Modular form 19950.2.a.ce

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 19950ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19950.cn4	19950ce1	\([1, 1, 1, 86537, 101272781]\)	\(4586790226340951/286015269335040\)	\(-4468988583360000000\)	\([4]\)	\(387072\)	\(2.2583\)	\(\Gamma_0(N)\)-optimal
19950.cn3	19950ce2	\([1, 1, 1, -2801463, 1735880781]\)	\(155617476551393929129/6633105589454400\)	\(103642274835225000000\)	\([2, 2]\)	\(774144\)	\(2.6048\)
19950.cn2	19950ce3	\([1, 1, 1, -7456463, -5535229219]\)	\(2934284984699764805929/851931751022747640\)	\(13311433609730431875000\)	\([2]\)	\(1548288\)	\(2.9514\)
19950.cn1	19950ce4	\([1, 1, 1, -44354463, 113679662781]\)	\(617611911727813844500009/1197723879765000\)	\(18714435621328125000\)	\([2]\)	\(1548288\)	\(2.9514\)