Elliptic curve isogeny class with Cremona label 91200ez (LMFDB label 91200.cp)

• Label: 91200ez
• Number of curves: $4$
• Conductor: $91200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 91200ez have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 91200ez do not have complex multiplication.

Modular form 91200.2.a.ez

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 91200ez

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91200.cp3	91200ez1	\([0, -1, 0, -2433, 40737]\)	\(389017/57\)	\(233472000000\)	\([2]\)	\(98304\)	\(0.90628\)	\(\Gamma_0(N)\)-optimal
91200.cp2	91200ez2	\([0, -1, 0, -10433, -367263]\)	\(30664297/3249\)	\(13307904000000\)	\([2, 2]\)	\(196608\)	\(1.2529\)
91200.cp4	91200ez3	\([0, -1, 0, 13567, -1831263]\)	\(67419143/390963\)	\(-1601384448000000\)	\([2]\)	\(393216\)	\(1.5994\)
91200.cp1	91200ez4	\([0, -1, 0, -162433, -25143263]\)	\(115714886617/1539\)	\(6303744000000\)	\([2]\)	\(393216\)	\(1.5994\)