Elliptic curve isogeny class with LMFDB label 51870.i (Cremona label 51870h)

• Label: 51870.i
• Number of curves: $4$
• Conductor: $51870$
• CM: no
• Rank: $1$

Elliptic curves in class 51870.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51870.i1	51870h4	\([1, 1, 0, -509238, 94409442]\)	\(14604525660045693247849/4583888290932309450\)	\(4583888290932309450\)	\([2]\)	\(1179648\)	\(2.2849\)
51870.i2	51870h2	\([1, 1, 0, -461988, 120652092]\)	\(10904788983938472043849/1966820496322500\)	\(1966820496322500\)	\([2, 2]\)	\(589824\)	\(1.9383\)
51870.i3	51870h1	\([1, 1, 0, -461968, 120663088]\)	\(10903372803697816092169/354790800\)	\(354790800\)	\([2]\)	\(294912\)	\(1.5918\)	\(\Gamma_0(N)\)-optimal
51870.i4	51870h3	\([1, 1, 0, -415058, 146191398]\)	\(-7907727847090108921129/4678297127978906250\)	\(-4678297127978906250\)	\([2]\)	\(1179648\)	\(2.2849\)

Rank

The elliptic curves in class 51870.i have rank \(1\).

Complex multiplication

The elliptic curves in class 51870.i do not have complex multiplication.

Modular form 51870.2.a.i

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.