Elliptic curve isogeny class with Cremona label 64896bd (LMFDB label 64896.bf)

• Label: 64896bd
• Number of curves: $2$
• Conductor: $64896$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 64896bd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 64896bd do not have complex multiplication.

Modular form 64896.2.a.bd

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 64896bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64896.bf2	64896bd1	\([0, 1, 0, -47038, 34210814]\)	\(-18629852000/808321761\)	\(-499406688114003072\)	\([2]\)	\(602112\)	\(2.0761\)	\(\Gamma_0(N)\)-optimal
64896.bf1	64896bd2	\([0, 1, 0, -1895053, 997765835]\)	\(9517173136000/62462907\)	\(4939719011102932992\)	\([2]\)	\(1204224\)	\(2.4227\)