Elliptic curve isogeny class with Cremona label 33462bp (LMFDB label 33462.ci)

• Label: 33462bp
• Number of curves: $4$
• Conductor: $33462$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 33462bp have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 33462bp do not have complex multiplication.

Modular form 33462.2.a.bp

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 33462bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33462.ci4	33462bp1	\([1, -1, 1, -14735, 687431]\)	\(2714704875/21296\)	\(2775376560528\)	\([2]\)	\(73728\)	\(1.2160\)	\(\Gamma_0(N)\)-optimal
33462.ci3	33462bp2	\([1, -1, 1, -24875, -371185]\)	\(13060888875/7086244\)	\(923506550515692\)	\([2]\)	\(147456\)	\(1.5625\)
33462.ci2	33462bp3	\([1, -1, 1, -98390, -11429531]\)	\(1108717875/45056\)	\(4280594010181632\)	\([2]\)	\(221184\)	\(1.7653\)
33462.ci1	33462bp4	\([1, -1, 1, -1558550, -748518299]\)	\(4406910829875/7744\)	\(735727095499968\)	\([2]\)	\(442368\)	\(2.1118\)