Elliptic curve isogeny class with Cremona label 3136t (LMFDB label 3136.m)

• Label: 3136t
• Number of curves: $4$
• Conductor: $3136$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 3136t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
3136.m4	3136t1	\([0, 0, 0, 49, 0]\)	\(1728\)	\(-7529536\)	\([2]\)	\(384\)	\(0.0089957\)	\(\Gamma_0(N)\)-optimal	\(-4\)
3136.m3	3136t2	\([0, 0, 0, -196, 0]\)	\(1728\)	\(481890304\)	\([2, 2]\)	\(768\)	\(0.35557\)		\(-4\)
3136.m1	3136t3	\([0, 0, 0, -2156, -38416]\)	\(287496\)	\(3855122432\)	\([2]\)	\(1536\)	\(0.70214\)		\(-16\)
3136.m2	3136t4	\([0, 0, 0, -2156, 38416]\)	\(287496\)	\(3855122432\)	\([2]\)	\(1536\)	\(0.70214\)		\(-16\)

Rank

The elliptic curves in class 3136t have rank \(1\).

Complex multiplication

Each elliptic curve in class 3136t has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 3136.2.a.t

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.