Elliptic curve isogeny class with Cremona label 78400dp (LMFDB label 78400.hw)

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

Rank

The elliptic curves in class 78400dp 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 78400.2.a.dp

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 78400dp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.hw2	78400dp1	\([0, 1, 0, -628833, -209185537]\)	\(-9317\)	\(-2951578112000000000\)	\([]\)	\(860160\)	\(2.2824\)	\(\Gamma_0(N)\)-optimal
78400.hw1	78400dp2	\([0, 1, 0, -16313708833, 801999742854463]\)	\(-162677523113838677\)	\(-2951578112000000000\)	\([]\)	\(31825920\)	\(4.0879\)