Elliptic curve isogeny class with Cremona label 338800bc (LMFDB label 338800.bc)

• Label: 338800bc
• Number of curves: $2$
• Conductor: $338800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 338800bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 338800bc do not have complex multiplication.

Modular form 338800.2.a.bc

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 338800bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338800.bc2	338800bc1	\([0, 1, 0, 214592, -3868812]\)	\(12829337821/7503125\)	\(-639146200000000000\)	\([2]\)	\(3686400\)	\(2.1060\)	\(\Gamma_0(N)\)-optimal
338800.bc1	338800bc2	\([0, 1, 0, -863408, -31896812]\)	\(835630707059/478515625\)	\(40761875000000000000\)	\([2]\)	\(7372800\)	\(2.4526\)