Properties

 Label 47040.dz Number of curves $4$ Conductor $47040$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dz1")

sage: E.isogeny_class()

Elliptic curves in class 47040.dz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47040.dz1 47040gk4 [0, 1, 0, -1171361, 487569375] [2] 589824
47040.dz2 47040gk2 [0, 1, 0, -73761, 7479135] [2, 2] 294912
47040.dz3 47040gk1 [0, 1, 0, -11041, -285601] [2] 147456 $$\Gamma_0(N)$$-optimal
47040.dz4 47040gk3 [0, 1, 0, 20319, 25335519] [2] 589824

Rank

sage: E.rank()

The elliptic curves in class 47040.dz have rank $$0$$.

Complex multiplication

The elliptic curves in class 47040.dz do not have complex multiplication.

Modular form 47040.2.a.dz

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 4q^{11} - 2q^{13} - q^{15} + 6q^{17} + O(q^{20})$$

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.