Elliptic curve isogeny class with Cremona label 11760cq (LMFDB label 11760.cg)

• Label: 11760cq
• Number of curves: $2$
• Conductor: $11760$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 11760cq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11760cq do not have complex multiplication.

Modular form 11760.2.a.cq

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 11760cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11760.cg1	11760cq1	\([0, 1, 0, -240, 468]\)	\(1092727/540\)	\(758661120\)	\([2]\)	\(4608\)	\(0.39701\)	\(\Gamma_0(N)\)-optimal
11760.cg2	11760cq2	\([0, 1, 0, 880, 4500]\)	\(53582633/36450\)	\(-51209625600\)	\([2]\)	\(9216\)	\(0.74359\)