Properties

 Label 3600.b Number of curves $2$ Conductor $3600$ CM $$\Q(\sqrt{-3})$$ Rank $1$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

Elliptic curves in class 3600.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
3600.b1 3600be1 $$[0, 0, 0, 0, -10000]$$ $$0$$ $$-43200000000$$ $$[]$$ $$2880$$ $$0.71964$$ $$\Gamma_0(N)$$-optimal $$-3$$
3600.b2 3600be2 $$[0, 0, 0, 0, 270000]$$ $$0$$ $$-31492800000000$$ $$[]$$ $$8640$$ $$1.2689$$   $$-3$$

Rank

sage: E.rank()

The elliptic curves in class 3600.b have rank $$1$$.

Complex multiplication

Each elliptic curve in class 3600.b has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-3})$$.

Modular form3600.2.a.b

sage: E.q_eigenform(10)

$$q - 5 q^{7} + 5 q^{13} + q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.