Elliptic curve isogeny class with LMFDB label 64980.bm (Cremona label 64980bi)

• Label: 64980.bm
• Number of curves: $4$
• Conductor: $64980$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 64980.bm have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 64980.bm do not have complex multiplication.

Modular form 64980.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 64980.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64980.bm1	64980bi4	\([0, 0, 0, -120071127, -506240114146]\)	\(21804712949838544/8680921875\)	\(76217543464608684000000\)	\([2]\)	\(9953280\)	\(3.3546\)
64980.bm2	64980bi3	\([0, 0, 0, -8646672, -5342619139]\)	\(130287139815424/52926616125\)	\(29043118367986164642000\)	\([2]\)	\(4976640\)	\(3.0080\)
64980.bm3	64980bi2	\([0, 0, 0, -4276767, 2541355526]\)	\(985329269584/252434475\)	\(2216347047850626374400\)	\([2]\)	\(3317760\)	\(2.8053\)
64980.bm4	64980bi1	\([0, 0, 0, -3968112, 3042179129]\)	\(12592337649664/1315845\)	\(722060938085766480\)	\([2]\)	\(1658880\)	\(2.4587\)	\(\Gamma_0(N)\)-optimal