Elliptic curve isogeny class with Cremona label 78400eu (LMFDB label 78400.ds)

• Label: 78400eu
• Number of curves: $2$
• Conductor: $78400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 78400eu have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 78400.2.a.eu

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.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 78400eu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.ds2	78400eu1	\([0, -1, 0, -12833, 613537]\)	\(-9317\)	\(-25088000000000\)	\([]\)	\(122880\)	\(1.3095\)	\(\Gamma_0(N)\)-optimal
78400.ds1	78400eu2	\([0, -1, 0, -332932833, -2338096546463]\)	\(-162677523113838677\)	\(-25088000000000\)	\([]\)	\(4546560\)	\(3.1149\)