Elliptic curve isogeny class with LMFDB label 3312.m (Cremona label 3312a)

• Label: 3312.m
• Number of curves: $2$
• Conductor: $3312$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 3312.m have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3312.m do not have complex multiplication.

Modular form 3312.2.a.m

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.

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

Isogeny graph

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

Elliptic curves in class 3312.m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3312.m1	3312a2	\([0, 0, 0, -10299, -402230]\)	\(80919167474/14283\)	\(21324404736\)	\([2]\)	\(3072\)	\(0.98678\)
3312.m2	3312a1	\([0, 0, 0, -579, -7598]\)	\(-28756228/16767\)	\(-12516498432\)	\([2]\)	\(1536\)	\(0.64021\)	\(\Gamma_0(N)\)-optimal