Elliptic curve isogeny class with LMFDB label 2912.c (Cremona label 2912a)

• Label: 2912.c
• Number of curves: $4$
• Conductor: $2912$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2912.c have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2912.c do not have complex multiplication.

Modular form 2912.2.a.c

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 2912.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2912.c1	2912a2	\([0, 0, 0, -971, -11646]\)	\(197747699976/91\)	\(46592\)	\([2]\)	\(576\)	\(0.23443\)
2912.c2	2912a3	\([0, 0, 0, -131, 310]\)	\(485587656/199927\)	\(102362624\)	\([4]\)	\(576\)	\(0.23443\)
2912.c3	2912a1	\([0, 0, 0, -61, -180]\)	\(392223168/8281\)	\(529984\)	\([2, 2]\)	\(288\)	\(-0.11214\)	\(\Gamma_0(N)\)-optimal
2912.c4	2912a4	\([0, 0, 0, 4, -544]\)	\(1728/31213\)	\(-127848448\)	\([2]\)	\(576\)	\(0.23443\)