Elliptic curve isogeny class with Cremona label 218400di (LMFDB label 218400.fo)

• Label: 218400di
• Number of curves: $4$
• Conductor: $218400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 218400di have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.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
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 218400di do not have complex multiplication.

Modular form 218400.2.a.di

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 218400di

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
218400.fo3	218400di1	\([0, 1, 0, -1058, -2112]\)	\(131096512/74529\)	\(74529000000\)	\([2, 2]\)	\(196608\)	\(0.77607\)	\(\Gamma_0(N)\)-optimal
218400.fo2	218400di2	\([0, 1, 0, -10808, 426888]\)	\(17454600584/93639\)	\(749112000000\)	\([2]\)	\(393216\)	\(1.1226\)
218400.fo4	218400di3	\([0, 1, 0, 4192, -12612]\)	\(1018108216/599781\)	\(-4798248000000\)	\([2]\)	\(393216\)	\(1.1226\)
218400.fo1	218400di4	\([0, 1, 0, -12433, -536737]\)	\(3321287488/7371\)	\(471744000000\)	\([2]\)	\(393216\)	\(1.1226\)