# Properties

 Label 3822t Number of curves $2$ Conductor $3822$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("t1")

E.isogeny_class()

## Elliptic curves in class 3822t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.s1 3822t1 $$[1, 1, 1, -22, -85]$$ $$-24100657/36504$$ $$-1788696$$ $$[]$$ $$1008$$ $$-0.10863$$ $$\Gamma_0(N)$$-optimal
3822.s2 3822t2 $$[1, 1, 1, 188, 1595]$$ $$14991903983/28960854$$ $$-1419081846$$ $$[]$$ $$3024$$ $$0.44067$$

## Rank

sage: E.rank()

The elliptic curves in class 3822t have rank $$1$$.

## Complex multiplication

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

## Modular form3822.2.a.t

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.