Properties

 Label 3822.t Number of curves $4$ Conductor $3822$ CM no Rank $0$ Graph

Related objects

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

E.isogeny_class()

Elliptic curves in class 3822.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.t1 3822x3 $$[1, 1, 1, -20434, -1132783]$$ $$8020417344913/187278$$ $$22033069422$$ $$[2]$$ $$9216$$ $$1.0969$$
3822.t2 3822x2 $$[1, 1, 1, -1324, -16759]$$ $$2181825073/298116$$ $$35073049284$$ $$[2, 2]$$ $$4608$$ $$0.75035$$
3822.t3 3822x1 $$[1, 1, 1, -344, 2057]$$ $$38272753/4368$$ $$513890832$$ $$[4]$$ $$2304$$ $$0.40378$$ $$\Gamma_0(N)$$-optimal
3822.t4 3822x4 $$[1, 1, 1, 2106, -85359]$$ $$8780064047/32388174$$ $$-3810436282926$$ $$[2]$$ $$9216$$ $$1.0969$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form3822.2.a.t

sage: E.q_eigenform(10)

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

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 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

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

The vertices are labelled with LMFDB labels.