Elliptic curve isogeny class with LMFDB label 366912.lm (Cremona label 366912lm)

• Label: 366912.lm
• Number of curves: $2$
• Conductor: $366912$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 366912.lm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 366912.lm do not have complex multiplication.

Modular form 366912.2.a.lm

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 366912.lm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
366912.lm1	366912lm2	\([0, 0, 0, -103708975692, -12855016276940432]\)	\(-5486773802537974663600129/2635437714\)	\(-59252741207985329012736\)	\([]\)	\(606928896\)	\(4.6085\)
366912.lm2	366912lm1	\([0, 0, 0, 20151348, -393401347472]\)	\(40251338884511/2997011332224\)	\(-67382027631432770022014976\)	\([]\)	\(86704128\)	\(3.6356\)	\(\Gamma_0(N)\)-optimal