# Properties

 Label 3822.w Number of curves $2$ Conductor $3822$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 3822.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.w1 3822v2 $$[1, 1, 1, -180050305, 929830670369]$$ $$-5486773802537974663600129/2635437714$$ $$-310056611614386$$ $$[]$$ $$395136$$ $$3.0195$$
3822.w2 3822v1 $$[1, 1, 1, 34985, 28472429]$$ $$40251338884511/2997011332224$$ $$-352595386224821376$$ $$[]$$ $$56448$$ $$2.0465$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3822.w have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3822.w do not have complex multiplication.

## Modular form3822.2.a.w

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 5q^{11} - q^{12} + q^{13} - q^{15} + q^{16} + 3q^{17} + q^{18} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 