Elliptic curve isogeny class with Cremona label 78400ju (LMFDB label 78400.fr)

• Label: 78400ju
• Number of curves: $2$
• Conductor: $78400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 78400ju 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 \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 78400ju do not have complex multiplication.

Modular form 78400.2.a.ju

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 78400ju

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.fr1	78400ju1	\([0, 0, 0, -392000, -94325000]\)	\(28311552/49\)	\(11529602000000000\)	\([2]\)	\(552960\)	\(1.9759\)	\(\Gamma_0(N)\)-optimal
78400.fr2	78400ju2	\([0, 0, 0, -269500, -154350000]\)	\(-574992/2401\)	\(-9039207968000000000\)	\([2]\)	\(1105920\)	\(2.3225\)