Elliptic curve isogeny class with Cremona label 371910cq (LMFDB label 371910.cq)

• Label: 371910cq
• Number of curves: $2$
• Conductor: $371910$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 371910cq have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 371910cq do not have complex multiplication.

Modular form 371910.2.a.cq

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 371910cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
371910.cq2	371910cq1	\([1, 0, 1, -93091598, -345739418944]\)	\(-758345163989747524609609/51164280992563200\)	\(-6019426494494067916800\)	\([2]\)	\(55148544\)	\(3.2341\)	\(\Gamma_0(N)\)-optimal
371910.cq1	371910cq2	\([1, 0, 1, -1489489678, -22126198111552]\)	\(3106332678537492823015958089/14138530560000\)	\(1663383981853440000\)	\([2]\)	\(110297088\)	\(3.5807\)