Elliptic curve isogeny class with Cremona label 37830w (LMFDB label 37830.y)

• Label: 37830w
• Number of curves: $4$
• Conductor: $37830$
• CM: no
• Rank: $1$

Elliptic curves in class 37830w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37830.y3	37830w1	\([1, 0, 0, -5337031, 4745226761]\)	\(16812135956704372661181169/1359700992000000\)	\(1359700992000000\)	\([4]\)	\(847872\)	\(2.3485\)	\(\Gamma_0(N)\)-optimal
37830.y2	37830w2	\([1, 0, 0, -5348551, 4723709705]\)	\(16921238277536807464708849/151160877562500000000\)	\(151160877562500000000\)	\([2, 2]\)	\(1695744\)	\(2.6951\)
37830.y4	37830w3	\([1, 0, 0, -1598551, 11223959705]\)	\(-451755260716342924708849/54162040664806200750000\)	\(-54162040664806200750000\)	\([2]\)	\(3391488\)	\(3.0417\)
37830.y1	37830w4	\([1, 0, 0, -9282871, -3153585799]\)	\(88464832782010227254086129/46900749206542968750000\)	\(46900749206542968750000\)	\([2]\)	\(3391488\)	\(3.0417\)

Rank

The elliptic curves in class 37830w have rank \(1\).

Complex multiplication

The elliptic curves in class 37830w do not have complex multiplication.

Modular form 37830.2.a.w

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.