Elliptic curve isogeny class with LMFDB label 67081.b (Cremona label 67081c)

• Label: 67081.b
• Number of curves: $4$
• Conductor: $67081$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $0$

Elliptic curves in class 67081.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
67081.b1	67081c4	\([1, -1, 1, -2494575, 1517046248]\)	\(16581375\)	\(103536315178307263\)	\([2]\)	\(709632\)	\(2.3258\)		\(-28\)
67081.b2	67081c3	\([1, -1, 1, -146740, 26640590]\)	\(-3375\)	\(-103536315178307263\)	\([2]\)	\(354816\)	\(1.9793\)		\(-7\)
67081.b3	67081c2	\([1, -1, 1, -50910, -4408330]\)	\(16581375\)	\(880044158287\)	\([2]\)	\(101376\)	\(1.3529\)		\(-28\)
67081.b4	67081c1	\([1, -1, 1, -2995, -76814]\)	\(-3375\)	\(-880044158287\)	\([2]\)	\(50688\)	\(1.0063\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 67081.b have rank \(0\).

Complex multiplication

Each elliptic curve in class 67081.b has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 67081.2.a.b

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.