Elliptic curve isogeny class with Cremona label 60480ec (LMFDB label 60480.m)

• Label: 60480ec
• Number of curves: $2$
• Conductor: $60480$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 60480ec have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 60480ec do not have complex multiplication.

Modular form 60480.2.a.ec

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 60480ec

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
60480.m1	60480ec1	\([0, 0, 0, -1188, -23112]\)	\(-9199872/6125\)	\(-123451776000\)	\([]\)	\(41472\)	\(0.82904\)	\(\Gamma_0(N)\)-optimal
60480.m2	60480ec2	\([0, 0, 0, 9612, 339768]\)	\(541416192/588245\)	\(-106706777103360\)	\([]\)	\(124416\)	\(1.3783\)