Elliptic curve isogeny class with Cremona label 49104bq (LMFDB label 49104.bv)

• Label: 49104bq
• Number of curves: $2$
• Conductor: $49104$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 49104bq have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 49104bq do not have complex multiplication.

Modular form 49104.2.a.bq

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 49104bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49104.bv1	49104bq1	\([0, 0, 0, -9003, 44890]\)	\(27027009001/15349092\)	\(45832143126528\)	\([2]\)	\(221184\)	\(1.3112\)	\(\Gamma_0(N)\)-optimal
49104.bv2	49104bq2	\([0, 0, 0, 35637, 357370]\)	\(1676253304439/988531038\)	\(-2951737862971392\)	\([2]\)	\(442368\)	\(1.6578\)