# Properties

 Label 3850.m Number of curves $2$ Conductor $3850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 3850.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.m1 3850p2 $$[1, 0, 0, -1838, -30458]$$ $$43949604889/42350$$ $$661718750$$ $$$$ $$3072$$ $$0.61370$$
3850.m2 3850p1 $$[1, 0, 0, -88, -708]$$ $$-4826809/10780$$ $$-168437500$$ $$$$ $$1536$$ $$0.26713$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3850.m have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3850.m do not have complex multiplication.

## Modular form3850.2.a.m

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} - q^{7} + q^{8} + q^{9} - q^{11} - 2q^{12} - 2q^{13} - q^{14} + q^{16} - 2q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 