Elliptic curve isogeny class with Cremona label 349690bm (LMFDB label 349690.bm)

• Label: 349690bm
• Number of curves: $2$
• Conductor: $349690$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 349690bm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 349690bm do not have complex multiplication.

Modular form 349690.2.a.bm

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 349690bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
349690.bm1	349690bm1	\([1, 1, 1, -21244396, -38308153971]\)	\(-1693700041/32000\)	\(-20034124031645919008000\)	\([]\)	\(32845824\)	\(3.0739\)	\(\Gamma_0(N)\)-optimal
349690.bm2	349690bm2	\([1, 1, 1, 84536829, -179039495711]\)	\(106718863559/83886080\)	\(-52518254101517877924331520\)	\([]\)	\(98537472\)	\(3.6232\)