Elliptic curve isogeny class with Cremona label 17689h (LMFDB label 17689.e)

• Label: 17689h
• Number of curves: $4$
• Conductor: $17689$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 17689h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
17689.e4	17689h1	\([1, -1, 1, -790, 10700]\)	\(-3375\)	\(-16136737183\)	\([2]\)	\(7200\)	\(0.67308\)	\(\Gamma_0(N)\)-optimal	\(-7\)
17689.e3	17689h2	\([1, -1, 1, -13425, 602018]\)	\(16581375\)	\(16136737183\)	\([2]\)	\(14400\)	\(1.0197\)		\(-28\)
17689.e2	17689h3	\([1, -1, 1, -38695, -3592802]\)	\(-3375\)	\(-1898470992842767\)	\([2]\)	\(50400\)	\(1.6460\)		\(-7\)
17689.e1	17689h4	\([1, -1, 1, -657810, -205176646]\)	\(16581375\)	\(1898470992842767\)	\([2]\)	\(100800\)	\(1.9926\)		\(-28\)

Rank

The elliptic curves in class 17689h have rank \(1\).

Complex multiplication

Each elliptic curve in class 17689h has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 17689.2.a.h

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.