Elliptic curve isogeny class with LMFDB label 3042.a (Cremona label 3042f)

• Label: 3042.a
• Number of curves: $3$
• Conductor: $3042$
• CM: no
• Rank: $0$

Elliptic curves in class 3042.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3042.a1	3042f3	\([1, -1, 0, -698931, 225080181]\)	\(-10730978619193/6656\)	\(-23420758473216\)	\([]\)	\(30240\)	\(1.8862\)
3042.a2	3042f2	\([1, -1, 0, -6876, 439128]\)	\(-10218313/17576\)	\(-61845440343336\)	\([]\)	\(10080\)	\(1.3369\)
3042.a3	3042f1	\([1, -1, 0, 729, -12609]\)	\(12167/26\)	\(-91487337786\)	\([]\)	\(3360\)	\(0.78755\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 3042.a have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3042.a do not have complex multiplication.

Modular form 3042.2.a.a

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.