Elliptic curve isogeny class with Cremona label 19600ea (LMFDB label 19600.q)

• Label: 19600ea
• Number of curves: $2$
• Conductor: $19600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 19600ea have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 19600ea do not have complex multiplication.

Modular form 19600.2.a.ea

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 19600ea

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19600.q2	19600ea1	\([0, 1, 0, 2042, -102537]\)	\(1280/7\)	\(-5147143750000\)	\([]\)	\(34560\)	\(1.1212\)	\(\Gamma_0(N)\)-optimal
19600.q1	19600ea2	\([0, 1, 0, -120458, -16150037]\)	\(-262885120/343\)	\(-252210043750000\)	\([]\)	\(103680\)	\(1.6705\)