Elliptic curve isogeny class with Cremona label 24960r (LMFDB label 24960.bp)

• Label: 24960r
• Number of curves: $2$
• Conductor: $24960$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 24960r have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 24960r do not have complex multiplication.

Modular form 24960.2.a.r

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 24960r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24960.bp1	24960r1	\([0, 1, 0, -88650, 7796250]\)	\(601942297084171232/141650616290625\)	\(18131278885200000\)	\([2]\)	\(179200\)	\(1.8314\)	\(\Gamma_0(N)\)-optimal
24960.bp2	24960r2	\([0, 1, 0, 206595, 48953403]\)	\(59519748892520576/97453916015625\)	\(-1596684960000000000\)	\([2]\)	\(358400\)	\(2.1780\)