Elliptic curve isogeny class with LMFDB label 38115.v (Cremona label 38115k)

• Label: 38115.v
• Number of curves: $4$
• Conductor: $38115$
• CM: no
• Rank: $1$

Elliptic curves in class 38115.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38115.v1	38115k4	\([1, -1, 0, -122535, -16477884]\)	\(157551496201/13125\)	\(16950517093125\)	\([2]\)	\(184320\)	\(1.5823\)
38115.v2	38115k2	\([1, -1, 0, -8190, -218025]\)	\(47045881/11025\)	\(14238434358225\)	\([2, 2]\)	\(92160\)	\(1.2357\)
38115.v3	38115k1	\([1, -1, 0, -2745, 53136]\)	\(1771561/105\)	\(135604136745\)	\([2]\)	\(46080\)	\(0.88914\)	\(\Gamma_0(N)\)-optimal
38115.v4	38115k3	\([1, -1, 0, 19035, -1377810]\)	\(590589719/972405\)	\(-1255829910395445\)	\([2]\)	\(184320\)	\(1.5823\)

Rank

The elliptic curves in class 38115.v have rank \(1\).

Complex multiplication

The elliptic curves in class 38115.v do not have complex multiplication.

Modular form 38115.2.a.v

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.