Elliptic curve isogeny class with LMFDB label 91200.iv (Cremona label 91200dz)

• Label: 91200.iv
• Number of curves: $4$
• Conductor: $91200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 91200.iv have rank \(1\).

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.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 91200.2.a.iv

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 91200.iv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91200.iv1	91200dz4	\([0, 1, 0, -182433, -30052737]\)	\(1311494070536/171\)	\(87552000000\)	\([2]\)	\(393216\)	\(1.5149\)
91200.iv2	91200dz2	\([0, 1, 0, -11433, -469737]\)	\(2582630848/29241\)	\(1871424000000\)	\([2, 2]\)	\(196608\)	\(1.1683\)
91200.iv3	91200dz3	\([0, 1, 0, -2433, -1180737]\)	\(-3112136/1172889\)	\(-600519168000000\)	\([2]\)	\(393216\)	\(1.5149\)
91200.iv4	91200dz1	\([0, 1, 0, -1308, 6138]\)	\(247673152/124659\)	\(124659000000\)	\([2]\)	\(98304\)	\(0.82174\)	\(\Gamma_0(N)\)-optimal