Elliptic curve isogeny class with Cremona label 34496p (LMFDB label 34496.bi)

• Label: 34496p
• Number of curves: $3$
• Conductor: $34496$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 34496p have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 34496p do not have complex multiplication.

Modular form 34496.2.a.p

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 34496p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
34496.bi3	34496p1	\([0, -1, 0, -65, -461]\)	\(-4096/11\)	\(-82824896\)	\([]\)	\(5760\)	\(0.20680\)	\(\Gamma_0(N)\)-optimal
34496.bi2	34496p2	\([0, -1, 0, -2025, 64219]\)	\(-122023936/161051\)	\(-1212639302336\)	\([]\)	\(28800\)	\(1.0115\)
34496.bi1	34496p3	\([0, -1, 0, -1532785, 730926659]\)	\(-52893159101157376/11\)	\(-82824896\)	\([]\)	\(144000\)	\(1.8162\)