Elliptic curve isogeny class with Cremona label 30752f (LMFDB label 30752.c)

• Label: 30752f
• Number of curves: $4$
• Conductor: $30752$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 30752f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
30752.c3	30752f1	\([0, 0, 0, -961, 0]\)	\(1728\)	\(56800235584\)	\([2, 2]\)	\(15360\)	\(0.75303\)	\(\Gamma_0(N)\)-optimal	\(-4\)
30752.c4	30752f2	\([0, 0, 0, 3844, 0]\)	\(1728\)	\(-3635215077376\)	\([2]\)	\(30720\)	\(1.0996\)		\(-4\)
30752.c1	30752f3	\([0, 0, 0, -10571, -417074]\)	\(287496\)	\(454401884672\)	\([2]\)	\(30720\)	\(1.0996\)		\(-16\)
30752.c2	30752f4	\([0, 0, 0, -10571, 417074]\)	\(287496\)	\(454401884672\)	\([2]\)	\(30720\)	\(1.0996\)		\(-16\)

Rank

The elliptic curves in class 30752f have rank \(1\).

Complex multiplication

Each elliptic curve in class 30752f has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 30752.2.a.f

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.