Elliptic curve isogeny class with Cremona label 64400ba (LMFDB label 64400.bd)

• Label: 64400ba
• Number of curves: $2$
• Conductor: $64400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 64400ba have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 64400ba do not have complex multiplication.

Modular form 64400.2.a.ba

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 64400ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
64400.bd2	64400ba1	\([0, 0, 0, -356075, 110932250]\)	\(-78013216986489/37918720000\)	\(-2426798080000000000\)	\([2]\)	\(774144\)	\(2.2332\)	\(\Gamma_0(N)\)-optimal
64400.bd1	64400ba2	\([0, 0, 0, -6244075, 6004820250]\)	\(420676324562824569/56350000000\)	\(3606400000000000000\)	\([2]\)	\(1548288\)	\(2.5798\)