Elliptic curve isogeny class with Cremona label 6120r (LMFDB label 6120.h)

• Label: 6120r
• Number of curves: $4$
• Conductor: $6120$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 6120r have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6120r do not have complex multiplication.

Modular form 6120.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 6120r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6120.h3	6120r1	\([0, 0, 0, -20658, -1142827]\)	\(83587439220736/6885\)	\(80306640\)	\([2]\)	\(6144\)	\(0.96032\)	\(\Gamma_0(N)\)-optimal
6120.h2	6120r2	\([0, 0, 0, -20703, -1137598]\)	\(5258429611216/47403225\)	\(8846579462400\)	\([2, 2]\)	\(12288\)	\(1.3069\)
6120.h1	6120r3	\([0, 0, 0, -36003, 768782]\)	\(6913728144004/3658971285\)	\(2731407428367360\)	\([2]\)	\(24576\)	\(1.6535\)
6120.h4	6120r4	\([0, 0, 0, -6123, -2709322]\)	\(-34008619684/4228250625\)	\(-3156372178560000\)	\([2]\)	\(24576\)	\(1.6535\)