Elliptic curve isogeny class with Cremona label 119658ce (LMFDB label 119658.cf)

• Label: 119658ce
• Number of curves: $2$
• Conductor: $119658$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 119658ce have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 119658ce do not have complex multiplication.

Modular form 119658.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 119658ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
119658.cf2	119658ce1	\([1, 1, 1, -2968568, -925065415]\)	\(24591016773082896625/11097062309363712\)	\(1305558283634331353088\)	\([2]\)	\(6082560\)	\(2.7470\)	\(\Gamma_0(N)\)-optimal
119658.cf1	119658ce2	\([1, 1, 1, -40098808, -97701322951]\)	\(60607987148648054544625/35377817158176768\)	\(4162164810842338578432\)	\([2]\)	\(12165120\)	\(3.0935\)